Vyxal 3, 18 bytes

-2 bytes by weird glyphs

'/6×⨪ᐕ6×DD⇄D:W4Y⎘”

Vyxal It Online!

<script type="vyxal3">
'/6×⨪ᐕ6×DD⇄D:W4Y⎘” ¶p
</script>
<script>
    args=[]
</script>
<script src="https://themoonisacheese.github.io/snippeterpreter/snippet.js" type="module"/>

Japt -R, 21 bytes

6Æ6ç"/\\"mp5)zXÑÃyËp4

Test it

Java 11, 148 122 113 bytes

v->{String a="/////",b="\\\\\\\\\\",t=(a+b).repeat(5)+"\n",u=(b+a).repeat(5)+"\n";t+=t+t+t+u+u+u+u;return t+t+t;}

-9 bytes thanks to @ceilingcat.

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Explanation:

v->{                     // Method with empty unused parameter & String return
  String a="/////",      //  Temp-String `a`, containing "/////"
         b="\\\\\\\\\\", //  Temp-String `b`, containing "\\\\\"
         t=              //  Temp-String `t`, containing:
           (a+b)         //   `a+b`
            .repeat(5)   //   Repeated 5 times
            +"\n"        //   With an additional newline
         u=              //  Temp-String `u`, containing:
           (b+a).repeat(5)+"\n";
                         //   Same as above, for `b+a` instead of `a+b`
         t+=             //  Append `t` with:
            t+t+t        //   Three times itself
            +u+u+u+u;    //   Followed by four times `u`
         return t+t+t;}  //  Then return three `t`-Strings appended together

Whitespace, 198 bytes

Commented version:

[N
S T	T	S N
call_A][N
S T	T	S N
call_A][N
S S T	S N
label_A][S S S T	S T	T	T	S S N
push_92_\][S S S T	S T	T	T	T	N
push_47_/][N
S T	T	N
call_B][N
S T	T	N
call_B][N
S T	T	N
call_B][N
S T	T	N
call_B][S N
T	swap][N
S T	T	N
call_B][N
S T	T	N
call_B][N
S T	T	N
call_B][N
S T	T	N
call_B][N
T	N
return][N
S S T	N
label_B][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][N
S T	N
call_C][S S S T	S T	S N
push_10][T	N
S S putchar][N
T	N
return][N
S S N
label_C][S N
S duplicate][S N
S duplicate][S N
S duplicate][S N
S duplicate][S N
S duplicate][T	N
S S putchar][T	N
S S putchar][T	N
S S putchar][T	N
S S putchar][T	N
S S putchar][S N
T	swap][N
T	N
return]

Try it online! (uncommented)

Perl 5, 49 bytes

//&say map$_/5%2+$'/4%2-1?'/':'\\',0..59for 0..23

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Raku (Perl 6) (rakudo), 68 bytes

say ((('/'x 5~'\\'x 5)x 6~"\n")x 4~(('\\'x 5~'/'x 5)x 6~"\n")x 4)x 3

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Python 2.7 66 56 55 bytes

new to code golfing

current version

a="/"*5+"\\"*5;print(4*(6*a+"\n")+4*(6*a[::-1]+"\n"))*3

Thanks Stewie Griffin

Forgot a silly whitespace ;)

66 byte version

a="/"*5+"\\"*5;b=a[::-1];c=6*a+"\n";d=6*b+"\n";e=4*c+4*d;print e*3

brainfuck, 116 bytes

+++++++++[->+>+++++<<]>+>+[->+>++<<]>+<<<<++++++[->++++[->>++++++[->.....>.....<<]<.<]>>>[-<+>]>[-<+>]<<[->>+<<]<<<]

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It took me some time to find this answer. I wanted to have an answer smaller than the current Java answer (120 bytes as of the time I'm writing this), and this is the best I was able to do. It may be possible to rearrange some values in order to obtain a smaller answer, but this is pretty good for now. Your turn, Java devs :)

AWK, 90 bytes

END{a="/////";for(b="\\\\\\\\\\";i++<6;)for(m=4;m--;print)for(z=6;z--;)printf i%2?a b:b a}

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Tcl, 97 bytes

proc r s\ n {string repe $s $n}
puts [r [r [r /////[r \\ 5] 6]\n 4][r [r [r \\ 5]///// 6]\n 4] 3]

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My try to outgolf myself didn't go well :( :

Tcl, 102 bytes

proc r s\ n {string repe $s $n}
proc R s\ t {r [r [r $s 5][r $t 5] 6]\n 4}
puts [r [R / \\][R \\ /] 3]

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05AB1E, 13 bytes

'/5׺6×4и»∊л

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Also works in the older legacy version of 05AB1E by replacing the º with ∞:
Try it online.

Explanation:

'/            '# Push "/"
  5×           # Repeat it 5 times as string: "/////"
    º          # Mirror it horizontally: "/////\\\\\"
     6×        # Repeat that 6 times as string
       4и      # Repeat that 4 times as list
         »     # Join this list with newline delimiter
          ∊    # Mirror it vertically
           Ð   # Triplicate this string
            »  # Join the three strings on the stack with newline delimiter
               # (after which it is output implicitly as result)

Regenerate, 44 bytes

((((/{5})(\\{5})){6}
){4}(($5$4){6}
){4}){3}

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Pretty straightforward use of groups and repetition. Group 4 is the five forward slashes and group 5 is the five backslashes; backreferencing them in the second set of lines saves one byte.

Bash, 120 109 bytes

z='/ \\'
f(){ printf $1$1$1$1$2$2$2$2;}
for i in {1..144};{
f $z;((i%6))||echo
((i%24))||z=${z#* }\ ${z% *}
}

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Vyxal j, 14 bytes

k/5•4ε:RJ6*3ẋf

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k/             # "/\"
  5•           # Repeat each char 5 times
    4ε         # Repeat 4 times
      :RJ      # Append a reversed copy
         6*    # Repeat each line six times
           3ẋf # Repeat the whole thing three times

x86-16 machine code, IBM PC DOS, 40 39 bytes

Binary:

00000000: b05c b118 b30c f6c1 0375 0234 73ba 0500  .\.......u.4s...
00000010: cd29 4a75 fb34 734b 75f3 50b0 0dcd 29b0  .)Ju.4sKu.P...).
00000020: 0acd 2958 e2de c3                        ..)X...

Listing:

B0 5C           MOV  AL, '\'        ; starting char
B1 18           MOV  CL, 24         ; CX = row counter 
            ROW: 
B3 0C           MOV  BL, 12         ; BX = pattern counter 
F6 C1 03        TEST CL, 3          ; have displayed 4 lines of same direction? 
75 02           JNZ  DIR            ; if not, continue with same 
34 73           XOR  AL, '/' XOR '\'; otherwise, swap the chars 
            DIR: 
BA 0005         MOV  DX, 5          ; DX = char counter 
            PATT: 
CD 29           INT  29H            ; write char to console 
4A              DEC  DX             ; have displayed 5 of the same? 
75 FB           JNZ  PATT           ; if not, keep writing  
34 73           XOR  AL, '/' XOR '\'; otherwise, swap the chars 
4B              DEC  BX             ; have displayed 12 patterns on a line? 
75 F3           JNZ  DIR            ; if not, keep writing patterns 
50              PUSH AX             ; otherwise, save the chars and write a CRLF
B0 0D           MOV  AL, 0DH        ; CR char 
CD 29           INT  29H            ; write to console 
B0 0A           MOV  AL, 0AH        ; LF char 
CD 29           INT  29H            ; write to console 
58              POP  AX             ; restore original chars 
E2 DE           LOOP ROW            ; loop until written 24 lines written 
C3              RET                 ; return to DOS

A standalone PC DOS executable COM program. Output to console:

Uiua 0.11.0, 20 bytes

+@/×45▽3⊂⟜¬↯4_60⊚5_5

See it in action

R, 72 65 bytes

write(matrix(c(x<-rep(c('/','\\'),24,,5),rev(x)),24,60),1,60,,'')

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builds a matrix of appropriate characters and writes it to stdout.

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SOML, 20 bytes

 /5* \5*+6*6{4{t}5{«

Explanation:

 /                    push "/", stack: ["/"]
  5*                  repeat it 5 times ["/////"]
     \                push "\" ["/////","\"]
      5*              repeat it 5 times ["/////","\\\\\"]
        +             add together ["/////\\\\\"]
         6*           repeat the string 6 times (it gets long here)
           6{         6 times repeat following code
             4{t}     output 4 times
                 5{«  put the 1st 5 chars at the end of the string

Charcoal, 26 bytes

ＵＯ⁵¦⁴/‖Ｍ↓→‖Ｍ↓→‖Ｍ‖ＢＯ²⁰‖ＢＯ↓⁸

Try it online! Link is to verbose version of code.

Explanation:

ＵＯ⁵¦⁴/  - drawing a 5 by 4 rectangle filled with /
‖Ｍ↓→            - reflect and mirror the canvas to the down and right direction (note that for this pattern order doesn't matter)
‖Ｍ             - reflect mirror without a argument (default is to the right, n times)
‖ＢＯ²⁰         - reflect butterfly overlap which would reflect the same thing n times to the left by default
‖ＢＯ↓⁸        - 8 characters but this time with a given direction which is down
 

Optimizing: -9, Thanks to @Neil for the help on reflects.

Nibbles, 13 bytes

^3`<^4`:;^6`<^5"/\\"\$

explanation

^3                     # replicate 3 times
  `<                   # sort
    ^4                 # replicate 4 times
      `:               # list of two lists (for getting newlines)
        ;              # let (save value to $)
         ^6            # replicate 6 times
           `<          # sort
             ^5        # replicate 5 times
               "/\\"   # the string /\
                    \$ # reverse the saved value

Note that that last $ can't be omitted because in the binary form the sort needs to place more data after its arg

MAWP, 88 bytes

3[4[6[5[68W1A;1A]%4[68W2A2W;1A]%1A]%52W;1A]4[6[5[68W2A2W;1A]%4[68W1A;1A]%1A]%52W;1A]%1A]

Try it!

Raise the max executions to at least 15000 to test it :D Oh, and be ready to wait for quite some time for it to finish.

MAWP 2.0, 61 bytes

3[4[6["/////\\\\\":1-]`10;1-]`4[6["\\\\\/////":1-]`10;1-]`1-]

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Add++ -i, 27 bytes

L,"/\"5€*6*b]4*d€bR+3*bUBJn

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The -i flag simply invokes the function with a clean stack and then outputs its return value.

How it works

L,		; Anonymous function
	"/\"	; Push this string			STACK = ["/\"]
	5€*	; Repeat each character 5 times		STACK = [["/////" "\\\\\"]]
	6*	; Repeat the array 6 times		STACK = [["/////" "\\\\\" "/////" "\\\\\" "/////" "\\\\\" "/////" "\\\\\" "/////" "\\\\\" "/////" "\\\\\"]]
	b]4*	; Repeat the whole thing 4 times	STACK = [[["/////" "\\\\\" ... "/////" "\\\\\"]]]
	d	; Duplicate				STACK = [[["/////" "\\\\\" ... "/////" "\\\\\"]] [["/////" "\\\\\" ... "/////" "\\\\\"]]]
	€bR	; Reverse the second copy		STACK = [[["/////" "\\\\\" ... "/////" "\\\\\"]] [["\\\\\" "/////" ... "\\\\\" "/////"]]]
	+	; Concatenate				STACK = [[["/////" "\\\\\" ...] ... [... "\\\\\" "/////"]]]
	3*	; Repeat 3 times			STACK = [[["/////" "\\\\\" ...] ... [... "\\\\\" "/////"]]]
	bUBJn	; Concatenate and grid			STACK = ["/////\\\\\...\\\\\/////"]

Pip -n, 24 bytes

(RF('/X6.'\X6)X24)X3<>72

Quad reflect is a bit weird in pip, so this answer uses normal reflect.

The -n flag joins lists with newlines.

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Canvas, 10 9 bytes

/５４＊╬６×３＊

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Explanation:

/          push "/"
 54*       extend horizontally 5 times and vertically 4 times
    ╬      quad-palindromize with 0 overlap
     6×    repeat horizontally 6 times
       3*  and again vertically, 3 times

Jstx, 21 bytes

♣/►\:►/;1BO♠/♦/!41o16

Not the shortest solution but I wanted to try this interesting challenge.

Explanation

♣  # Push literal 5
/  # Enter an iteration block over the first stack value.
►\ # Push literal \
:  # Push the sum of the second and first stack values.
►/ # Push literal /
;  # Push the difference of the second and first stack values.
1  # End an iteration block.
B  # Push five copies of the first stack value.
O  # Collapse all stack values into a string, then Push that string.
♠  # Push literal 6
/  # Enter an iteration block over the first stack value.
♦  # Push literal 4
/  # Enter an iteration block over the first stack value.
!  # Push a copy of the first stack value.
4  # Print the first stack value, then a newline.
1  # End an iteration block.
o  # Push the first stack value with characters in reverse order.
1  # End an iteration block.
6  # Ends program execution.

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Excel (loaded with VBA), 70 62 bytes

Formula for each cell (A4 through BH27):

=IF(SIN(COLUMN()*0.62)*SIN(ROW()*0.8)>0,"\","/")

I'm not sure how to score this and I couldn't find a consensus. It's a 48 byte pure Excel formula, the same in every cell (but of course the fact that it should be in a particular range is also information). It takes 62 bytes to load it by executing this in the VBA Immediate window.

[A4:BH27]="=IF(SIN(COLUMN()*.62)*SIN(ROW()*.8)>0,""\"",""/"")" 

Output

Pyth, 21 20 bytes

J*6S*5"/\\"V6V4J)=_J

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J=6*sorted(5*"/\\")
for N in range(6):
    for N in range(4):
        print(J)
    J=J[::-1]

///, 116 bytes

/a/\\\\\\\\\\\\\\\///b/\\\\\\\\\\\\\\\\//A/aaaaa//B/bbbbb//C/ABABABABABAB
//D/BABABABABABA
/CCCCDDDDCCCCDDDDCCCCDDDD

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Edit: the \\\\\\\\\\\\\\\/ and \\\\\\\\\\\\\\\\ are actually a single / and \, respectively.

Edit: -3 because I thought of removing i. I think this can't be further golfed.

SOGL V0.12, 11 bytes

└5*5∙╬¡6*3∙

Try it Here!

Explanation:

└            push "/"
 5*          repeat 5 times
   5∙        repeat vertically 5 times
     έ      quad-palindromize with 0 overlap and mirroring characters
       6*    multiply 6 times horizontally
         3∙  multiply 3 times vertically

Python 2, 83 55 bytes

x=('/'*5+'\\'*5)*6;print((x+'\n')*4+(x[::-1]+'\n')*4)*3

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-28 bytes thanks to Leaky Nun

T-SQL, 113 bytes

DECLARE @ INT=0L:IF @%8<4PRINT REPLICATE('/////\\\\\',6)ELSE PRINT REPLICATE('\\\\\/////',6)SET @+=1IF @<24GOTO L

Formatted:

DECLARE @ INT=0
L:
   IF @%8<4 PRINT REPLICATE('/////\\\\\',6)
   ELSE PRINT REPLICATE('\\\\\/////',6)
   SET @+=1
IF @<24 GOTO L

Using both string literals seems to be the shortest option, trying to REPLICATE(REPLICATE('/',5)+REPLICATE('\',5) is way longer, as is using additional variables.

Ruby, 83 + 14 = 97 bytes

puts Zlib.inflate Base64.decode64"eNrTB4EYECCdxTVENSP4pLOGqubhE8+j8Twaz6PxDAA3Pofw"

Add 14 bytes for -rzlib and -rbase64 flags.

Perl, 51 50 bytes

Perl 5.10.0+:

perl -E 'say+((@_=("/"x5,"\\"x5)x6,$/)x4,(pop@_,@_,$/)x4)x3'

Perl before 5.10.0 (52 bytes):

perl -e 'print+((@_=("/"x5,"\\"x5)x6,$/)x4,(pop@_,@_,$/)x4)x3'

Ungolfed:

say(
    (
        (
            @_ = ('/' x 5, '\\' x 5) x 6,
            $/,  # new line symbol
        ) x 4,
        (
            pop(@_),
            @_,
            $/,
        ) x 4,
    ) x 3
);

Thanx to @DomHastings for 1 byte.

PHP, 142 124 bytes

<?=str_replace(['#','-'],['/////','\\\\\\\\\\'],wordwrap(str_repeat(str_repeat("#-",24).str_repeat("-#",24), 4),12,"\n",1));

Previous version:

<?for($i=1;$i<4;$i++)echo wordwrap(str_repeat("/////\\\\\\\\\\",24),60,"\n",1)."\n".wordwrap(str_repeat("\\\\\\\\\\/////",24),60,"\n",1)."\n";

Output:

C:\PHP\>php this-is-my-pillow.php
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////

Lithp, 166 characters

Line split for readability.

#::((def x #S,N::(invoke S repeat N))(var A (x "/" 5))(var B (x "\\" 5))
(var C (+ (x (+ A B) 6) (nl)))(var D (+ (x (+ B A) 6) (nl)))
(print (x (+ (x C 4) (x D 4)) 5)))

Sample usage:

% pillow.lithp
(
    (def f #::((def x #S,N::(invoke S repeat N))(var A (x "/" 5))(var B (x "\\" 5))(var C (+ (x (+ A B) 6) (nl)))(var D (+ (x (+ B A) 6) (nl)))(print (x (+ (x C 4) (x D 4)) 5))))
    (f)
)

Run with:

./run.js pillow.lithp

This is a fairly simple solution that repeats characters. There is no standalone repeat function yet, so invoke is used to call "string".repeat(N) and adds a bit to the count.

C++ 138

void P(){int i,j,k,l;for(i=0;i<3;i++)for(j=0;j<8;j++)for(k=0;k<12;k++)for(l=0;l<5;l++)cout<<((j/4)?(k%2)?'/':'\\':(k%2)?'\\':'/')<<'\n';} 

Ungolfed

#include<conio.h>
#include<iostream>
using namespace std;

void P()
{
    int i,j,k,l;
    for(i=0;i<3;i++)
        for(j=0;j<8;j++)
            for(k=0;k<12;k++)
                for(l=0;l<5;l++)
                    cout<<((j/4)?(k%2)?'/':'\\':(k%2)?'\\':'/')<<'\n';
}

int main()
{
    P();
    _getch();
    return 0;
}

V, 22 21 bytes

Edit One byte won, thanks @DjMcMayhem:

5á\5á/05ä$4Ä5x$p4Ä3ä}

Changes are:

• Y4P -> 4Ä Use V duplicate line instead of Vim built-in command (this will add a blank line at the end of the paragraph)
• 3äG -> 3ä} Duplicate the paragraph instead of the whole buffer (to avoid blank line generated by previous change)

Original post

5á\5á/05ä$Y4P5x$p4Ä3äG

Try it online

Decomposed like this:

5á\                    Write 5 \
   5á/                 Write 5 / after
      0                Go to the beginning of the line
       5ä$             Copy the text to the end of the line and repeat it 5 times
          Y4P          Copy the line and create 4 new copies
             5x$p      Delete the 5 first characters and put them at the end of the line
                 4Ä    Duplicate this line
                   3äG Duplicate the whole text

Julia, 56 bytes

a="////\\\\\\\\"^6*"\n";print((a^4*a[[48:-1:1,49]]^4)^3)

Brainfuck, 179 bytes

->++++++++[-<++++++>]++>+++++++++[-<++++++++++>]++++++++++>>>>+++[-<++++[-<++++++[-<+++++[-<<<.>>>]+++++[-<<.>>]>]<<.>>>]++++[-<++++++[-<+++++[-<<.>>]+++++[-<<<.>>>]>]<<.>>>]>]

I know this isn't the best score in the thread but I wanted to try out brainfuck and give this a try.

Edit: I must've made an error while copypasting. This version should work

Brainfuck, 168 bytes

++++++[>++++++++<-]>-<+++++++++[>>++++++++++<<-]>>++<<+++++[>>>++<<<-]>>>>+++[>++++[>++++++[<<<<<.....>.....>>>>-]<<<.>>-]++++[>++++++[<<<<.....<.....>>>>>-]<<<.>>-]<-]

MATLAB, 58 44 bytes

Thanks to @Stewie Griffin for saving a bunch of bytes ;)

[repmat(kron(['/\';'\/'],ones(4,5)),3,6),'']

Old version:

p=@()char(47+45*kron(ones(3,6),kron([0 1;1 0],ones(4,5))))

Powershell, 77 bytes

I must say I thought this would be easier with PowerShell, but it's quite hard to create something more condense than this.

$a=@("/","\");"$(1..6|%{1..3|%{1..6|%{$a[$b]*5;$a[!$b]*5};"rn"}; $b=!$b})"

More readable:

$a=@("/","\")
"$(1..6|%{
    1..3|%{ 
     1..6|%{
     $a[$b]*5
     $a[!$b]*5
        }
     "`r`n"}
    $b=!$b})"

I'm using the index numbers of the array in order to decide whether I should put \ or / and between every loop I simply toggle the variable.

Brainfuck, 149 bytes

++++++++++>++++++[>++++++++<-]>->+++++++++[>++++++++++<-]>++>+++[<<++++[<<++++++[>.....>>.....<<<-]<.>>>-]++++[<<++++++[>>>.....<<.....<-]<.>>>-]>>-]

The best interpreter EVAR!

This uses 6 cells (no wrapping, no modulo). Here they are:

0A 00 2F 00 5C 00

The 00 cells are used for the loop counters. Here, the counters are filled in with initial values:

0A 06 2F 04 5C 03

The leftmost counter is for the innermost loop (yes, I use nested loops of depth 3). Please note that the 4th cell (04 counter) is used twice, once for /////\\\\\..., and once for \\\\\/////... every time.

0A, 2F and 5C are the characters \n, / and \, respectively.

Pyth, 49 48 40 37 34 bytes

J60K*24+*5\/*5\\V24:*3+K_K*JN+J*JN

OK, I'm just learning Pyth so this is a direct port of my Python answer. Still a lot of golfing to do but it works so I am posting it anyway. Any hints gratefully received :)

1 byte saved with thanks to @Flp.Tkc

-8 by working out how to do it with a variable

-3 by moving the *24 to the assignment of K

-3 by getting rid of the quotes

Python 2, 86 80 76 74 73 bytes

for z in range(24):a=('/'*5+'\\'*5)*24;print((a+a[::-1])*3)[z*60:z*60+60]

Could probably golf a few more off it but it's a start.

Edit

Saved 6 by removing some unneeded brackets

Another 4 by using a single string and then reversing it

Thanks @Adnan. Had a late night last night and still not fully awake yet :p

-1 by moving the *24 to the variable instead of using it twice

05AB1E, 15 bytes

„/\5×{R6×6FR4F=

Try it online!

Explanation:

„/\             # Push "/\"
   5×           # Repeat string five times: "/\/\/\/\/\"
     {          # Sort: "/////\\\\\"
      R         # Reverse: "\\\\\/////
       6×       # Repeat string six times
         6F     # Repeat the following six times:
           R    #   Reverse
            4F  #   Repeat the following four times:
              = #     Print without popping

Uses the CP-1252 encoding.

Pyth, 22 bytes

V6V4V12p*5?%+bN2\\\/)k

Try it here.

Explanation:

V6                     Loop 6 times, with N from 0 to 5:
  V4                   Loop 4 times, with H from 0 to 3:
    V12                Loop 12 times, with b from 0 to 11:
      p                Print without newline
        *              The repetition
          5            5 times of
          ?            if
            %          the remainder
              + b N    when the sum of b and N
              2        is divided by 2
          \\           then the "\" character
          \/           else the "/" character
    )                  End
                       (implicitly print with newline)
  k                    k (empty string)
                       (implicit end)
                       (implicit end)

Sorry if the explanation is a little hard to understand, but it was kinda complicated.

Befunge-98, 76 bytes

'/\::2%0`!\4c*/2%0`!-> #0 #\ #\' $ #\_\3k:4k,1+:c%0`!> #0 #, #a_:cad+*\`!#@_

TryItOnline!

String processing/generation can be difficult with only a stack available...

A couple bytes may be able to be shaved off here or there, but I beat brainfuck, so I'm happy.

Explanation

Push '/' on the stack
Swap top two (at the beginning, zero will now be on top). Call top = iterator = n
Calculate (n % 2 == 0) != ((n / 48) % 2 == 0)
If true, swap top two, replace '/' with '\', swap again
Swap top two (so that we now have the character to print on top, followed by n)
Duplicate the char 4 times, and print 5 times
Increment n
If n % 12 == 0, print a newline character
If !(288 > n), end, else repeat

Vim, 44 27 bytes

EDIT Lot of bytes won thanks to @DrMcMoylex:

5i\<esc>5a/<esc>0y$5PY4P5x$pY3PyGPP

Original answer:

I'm not sure that really fits the rules of this site but I thought that was fun to try it:

i\<esc>59.:s;\v(.{5})\1;\1/////;g<CR>Y4P5x$pY3PyGPP

Which can be decomposed like this:

i\<esc>                       Insert a \
59.                           Repeat 59 time the insertion
:s;\v(.{5})\1;\1/////;g<CR>   Match 5 characters followed by the same 5 characters
                              And replace them by these 5 characters followed by 5 /
Y4P                           Copy the line and repeat it 4 times
5x$p                          On the current line delete 5 characters and put them 
                              at the end of the line
Y3P                           Copy the line and repeat it 3 times
yG                            Copy all the lines
PP                            Repeat them 2 times

Java 7, 120 bytes

String c(){String r="";for(int i=0;i<1440;r+=(i%60<1?"\n":"")+(i/60%8<4?i%10<5?"/":"\\":i%10<5?"\\":"/"),i++);return r;}

Pushed everything into one loop. Beats Brainfuck, mission accomplished.

See it online: https://ideone.com/pZjma3

Brainfuck, 140 bytes

>>>++++++++[>++++++>++++++++++++<<-]++++++++++>->----<<<<<+++[>++++[>++++++[>>.....>.....<<<-]>.<<-]++++[>++++++[>>>.....<.....<<-]>.<<-]<-]

:-D

Python 3, 60 bytes

Lots of multiplying strings!

print((((('/'*5+'\\'*5)*6+'\n')*4)+(('\\'*5+'/'*5)*6+'\n')*4)*3)

Output

/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////

PowerShell v2+, 44 bytes

,(,('/////\\\\\'*6)*4+,('\\\\\/////'*6)*4)*3

Abuses the crap outta the default Write-Output behavior to put a newline between elements.

Explanation

I'm also trying out a new explanation format, rather than the long prose I traditionally write.

,(,('/////\\\\\'*6)*4+,('\\\\\/////'*6)*4)*3
    '/////\\\\\'*6                            # Repeat this string 6 times
  ,(              )*4                         # Repeat it into an array of four elements
                     +                        # Array concatenate with
                      ,('\\\\\/////'*6)*4)    # The same with the slashes the other way
,(                                       )*3  # Repeat it into an array of three elements
                                              # (i.e., 24 total strings)

APL, 16

4⌿5/1↓⍉12 7⍴'\/'

Try it on tryapl.org

PHP, 55 bytes

for(;$i<1440;)echo"/\\"[($i/5^$i/240)&1],"\n"[++$i%60];

toggles between forward and backward slash every 5 characters, inverted every 240 characters;
not counting newlines; newlines inserted every 60 characters.

has one trailing newline. Run with -r.

recursive program for 66 bytes:

<?="/\\"[($i/5^$i/240)&1]."\n"[++$i%60];if($i<1440)include"p.php";

save to file p.php; call from CLI (or insert ($i?"":"<pre>"). after <?=)

GolfSharp, 59 bytes

r(0,1440).s(n=>n%10<5^n%480<240?"\\":"/").j().S(60).j("\n")

Python 2, 49 bytes

b,a='\/';exec("print(a*5+b*5)*6;"*4+"a,b=b,a;")*6

Thanks to Mitch Schwartz for this clean method that saves a byte. The idea is to print four lines of ('\\'*5+'/'*5)*6, swap the roles of slash and backslash, and then do that whole process 6 times. The two characters are stored in a and b, and swapped as a,b=b,a. The double-loop is double by generating the following code string, then executing it with exec:

print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;a,b=b,a;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;a,b=b,a;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;a,b=b,a;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;a,b=b,a;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;a,b=b,a;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;print(a*5+b*5)*6;a,b=b,a;

50 bytes:

s='/'*5+'\\'*5;exec("print s*6;"*4+"s=s[::-1];")*6

Makes the line string, prints it four times and then reverses it, then does that 6 times. Does so by generating the following code, then executing it:

print s*6;print s*6;print s*6;print s*6;s=s[::-1];print s*6;print s*6;print s*6;print s*6;s=s[::-1];print s*6;print s*6;print s*6;print s*6;s=s[::-1];print s*6;print s*6;print s*6;print s*6;s=s[::-1];print s*6;print s*6;print s*6;print s*6;s=s[::-1];print s*6;print s*6;print s*6;print s*6;s=s[::-1]

Here are some of the iterations of my golfing:

for c in([1]*4+[-1]*4)*3:print('/'*5+'\\'*5)[::c]*6

for i in range(24):print('/\\'*5+'\/'*5)[i/4%2::2]*6

for c in range(24):print('\\'*5+'/'*5)[::(c&4)/2-1]*6

for i in range(24):print('/'*5+'\\'*5)[::1-i/4%2*2]*6

for c in([1]*4+[0]*4)*3:print('\/'*5+'/\\'*5)[c::2]*6

for c in([1]*4+[0]*4)*3:print('\/'[c]*5+'/\\'[c]*5)*6

for c in(['/\\']*4+['\/']*4)*3:print(c[0]*5+c[1]*5)*6

for c in([5]*4+[-5]*4)*3:print('/'*c+'\\'*5+'/'*-c)*6

print((('/'*5+'\\'*5)*6+'\n')*4+(('\\'*5+'/'*5)*6+'\n')*4)*3

for x in(['/'*5+'\\'*5]*4+['\\'*5+'/'*5]*4)*3:print x*6

a='/'*5;b='\\'*5
for x in([a+b]*4+[b+a]*4)*3:print x*6

s='/'*5+'\\'*5
for x in([s]*4+[s[::-1]]*4)*3:print x*6

s=('/'*5+'\\'*5)*9
exec("print s[:60];"*4+"s=s[5:];")*6

a='/'*5;b='\\'*5
for i in range(24):print[a+b,b+a][i/4%2]*6

Swift 3, 100 99 97 bytes

var a="/////",b="\\\\\\\\\\",c=""
(1...144).map{c+=a+b+($0%6<1 ?"\n":"")
$0%24<1 ?swap(&a,&b):()}

Could save 1 byte if Swift print function did not add a newline by default.

Edit 1:

Saved 1 byte by changing the if to ternary

if(i%24<1){swap(&a,&b)} -> i%24<1 ?swap(&a,&b):()

Edit 2:

Changed from for to map over the CountableClosedRange

Racket 156 bytes

(define g #t)(for((k 24))(for((i 12))(for((j 5))(display(if g "/""\\")))(set! g(if g #f #t)))
(when(= 0(modulo(add1 k)4))(set! g(if g #f #t)))(displayln""))

Ungolfed:

(define(f)
  (define g #t)
  (for ((k 24))
    (for ((i 12))
      (for ((j 5))
        (display (if g "/" "\\")))
      (set! g (if g #f #t)))
    (when (= 0 (modulo (add1 k) 4))
      (set! g (if g #f #t)))
    (displayln "")))

Testing:

(f)

Output:

/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////

MATL, 18 16 bytes

'\/'6:&+thK5&Y")

Try it online!

Explanation

'\/'   % Push this string
6:     % Push array [1 2 3 4 5 6]
&+     % 6×6 matrix with all pair-wise additions from that array
th     % Concatenate horizontally with itself. Gives a 6×12 matrix
K      % Push 4
5      % Push 5
&Y"    % Repeat each entry of the matrix 4 times vertically and 5 times horizontally
       % This gives a 24×60 matrix
)      % Index (modularly) into the string. This produces the desired 24×60 char array

C, 66 61 bytes

5 bytes saved thanks to orlp.

Straightforward character by character printing. 61 characters per row, last is newline (ASCII 10) and the others alternate between /47 and \ 92.

i;f(){for(i=1463;i;)putchar(i--%61?i%61/5+i/244&1?92:47:10);‌​}

//call like this
main(){f();}

GameMaker Language, 104 bytes

You should make sure that uninitialized variables don't throw an error. This setting is in the main page of Preferences. Otherwise, add e='' to the beginning of the program.

a="/////"b="\\\\\"d=b+a+b+a+b+a+b c=a+d d+=a for(i=0;i<24;i++)if i mod 8>3e+=d else e+=c e+="#" return e

P.S. Yes, each part of the for loop needs an expression. So I can't for(i=0;i<24;) and have i++ later.

Output

/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////

Batch, 132 bytes

@set s=/////\\\\\
@set s=%s%%s%%s%%s%%s%%s%
@set s=%s% %s:~5%/////
@for %%s in (%s% %s% %s%)do @for /l %%i in (1,1,4)do @echo %%s

Works by building up the two types of row, then looping through six rows four times per row.

PHP, 73 69 bytes

for($s='/\\';$i<1440;$i++)echo$i%60<1?'
':'',$s[($i/5+($i/240|0))%2];

Demo

http://ideone.com/z7N1Md

C#, 126 Bytes

var s="";var c="/";for(int a=0;a<24;){for(int b=0;b<60;)s+=b++%5>0?c:c=="/"?c=@"\":c="/";s+="\n";c=a++%3>1?c=="/"?@"\":"/":c;}

string s is output. It could be 3 byte less, when it is infinite.

Ungolfed

        var s = "";
        var c = "/";
        for (int a = 0; a < 24;)
        {
            for (int b = 0; b < 60;)//write line
            {
                s += b++ % 5 > 0 ? c : c == "/" ? c = @"\" : c = "/";//Change  /to \ and vice versa after five times
            }
            s += "\n";


            c = a++ % 3 > 1 ? c == "/"? c = @"\" : c = "/" :c; //Change  /to \ and vice versa after three lines
        }

APL, 30 bytes

A←240⍴'/////\\\\\'⋄24 60⍴A,⊖A

I'm quite new to APL, (I'm using APLX, but this should work across most implementations of APL), so this is a quite simplistic solution.

Explanation:

A ← 240 ⍴ '/////\\\\\' ⍝ set A to be a 240 character vector populated with '/////\\\\\'
⋄                      ⍝ statement separator
24 60 ⍴ A,⊖A           ⍝ populate a 24 by 60 character matrix with the concatenation 
                          of A and the reverse of A (⊖A)

Pyth, 24 bytes

Jj*4[*6+*5\/*5\\;j*3[J_J

Try it!

Explanation:

Jj*4[*6+*5\/*5\\;j*3[J_J
   4                     4
      6                  6
         5               5
          \/             "/"
        *                Repeat
             5           5
              \\         "\\"
            *            Repeat
       +                 Concatenate
     *                   Repeat
    [                    List
  *                      Repeat
 j                       Join
J                        Assign copy to J
                ;        Close argument list
                   3     3
                     J   J
                       J J
                      _  Reverse
                    [    List
                  *      Repeat
                 j       Join

Pyke, 16 bytes

"/\"6*5m*n+4*sD3

After update today that allowed " in string literals, 17 bytes

"/\\"6*5m*n+4*sD3

Try it here!

Vitsy, 28 26 bytes

This can be golfed a bit.

'\/'6\[4\[c\[4\[DO]r]aO]r]

Try it online!

Octave, 50 48 bytes

Anonymous function:

@()repmat([A=repmat(47,4,5) B=A*2-2;B A ''],3,6)

You can try online here. Simply run the above command and then run the function with ans().

Essentially this creates an array of the value 47 which is 4 high and 5 wide. It then creates a second array of value 92 which is the same size.

The two arrays are concatenated into a checkerboard of [A B;B A]. The '' is concatenated as well to force conversion to character strings.

Finally the whole array is replicated 3 times down and 6 times across to form the final size.

• Saved 2 bytes, thanks @StewieGriffin

CJam, 24 23 bytes

"/\\"5e*6*]4*N*_W%]3*N*

ONLINE

Thanks 8478 (Martin Ender) for -1.

Explanation:

"/\\"5e*6*]4*N*_W%]3*N* Code
"/\\"                   Push "/\\"
     5                  Push 5
      e*                Repeat each
        6               Push 6
         *              Repeat
          ]             Wrap stack from [ to ToS in array
           4            Push 4
            *           Repeat
             N          Push N = "\n"
              *         Join
               _        Duplicate
                W       Push W = -1
                 %      Take every nth item
                  ]     Wrap stack from [ to ToS in array
                   3    Push 3
                    *   Repeat
                     N  Push N = "\n"
                      * Join

J, 31 28 19 bytes

4#_60]`|.\5#72$'/\'

Usage

   4#_60]`|.\5#72$'/\'
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////

Bubblegum, 30 bytes

00000000: d307 8118 1020 9dc5 3544 3523 f8a4 b386  ..... ..5D5#....
00000010: aae6 e113 cfa3 f13c 1acf a3f1 0c00       .......<......

Obligatory Bubblegum answer.

Ruby, 46 bytes

Creates the following string (70 characters, one set more than needed) then alternates between sampling characters 0..59 and 5..64from it.

/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\

code and output

24.times{|i|puts ((?/*5+?\\*5)*7)[i/4%2*5,60]}

/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////
\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////

interesting mistake (a 7 instead of a 5)

24.times{|i|puts ((?/*5+?\\*5)*7)[i/4%2*7,60]}

/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\
\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\\\\/////\\

JavaScript (ES6), 68 60 58 bytes

A recursive function. Several optimizations inspired from chocochaos answer.

f=(n=1440)=>n--?'/\\'[n/240&1^n/5&1]+(n%60?'':`
`)+f(n):''

Demo

f=(n=1440)=>n--?'/\\'[n/240&1^n/5&1]+(n%60?'':`
`)+f(n):''

console.log(f());

Dyalog APL, 24 bytes

(60⍴5/0 4)⊖60/⍪∊3⍴⊂4/'/\'

05AB1E, 18 15 bytes

Code:

„/\5×{4Å6×»6F=R

Explanation:

„/\               # Push the string "/\"
   5×             # Repeat 5 times: "/\/\/\/\/\"
     {            # Sort, resulting in: "/////\\\\\"
      4Å6         # Create a list of 6's with length 4: [6, 6, 6, 6]
         ×        # Vectorized string multiplication
          »       # Join by newlines
           6F     # Do the following six times..
             =    #   Print with a newline without popping
              R   #   Reverse the string

Uses the CP-1252 encoding. Try it online!

Haskell, 77 70 57 bytes

a%b=(<*[1..a]).([1..b]>>)
unlines$4%3$5%6<$>["/\\","\\/"]

Boring concats and replicates instead of playing with sines. Old was:

unlines[["\\/"!!(ceiling$sin(pi*x/5)*sin(pi*y/4))|x<-[0.5..59]]|y<-[0.5..23]]

Self-modifying Brainfuck, 91 bytes

>>+++[<++++[<++++++[<.....<.....>>-]<<<.>>>>-]++++[<++++++[<<.....>.....>-]<<<.>>>>-]>-]
\/

Try it online!

Same as my brainfuck answer, but uses the 3 last characters of the source code instead of generating them at runtime.

Actually, 21 bytes

"/\"5*SR6*;4α@R4α+3αi

Try it online!

-1 byte from Adnan

Explanation:

"/\"5*SR6*;4α@R4α+3αi
"/\"5*                 "/\" repeated 5 times
      SR               sort and reverse (result: "\\\\\/////")
        6*             repeat string 6 times (forms one row)
          ;4α          copy and push a list containing 4 copies
             @R4α+     push a list containing 4 copies of the reversed string, append to previous list (now we have one row of diamonds)
                  3α   repeat pattern vertically 2 more times
                    i  flatten and implicitly print

Jelly, 17 16 bytes

⁾/\ẋ6Wẋ4;U$ẋ3x5Y

Try it online!

Thanks to 6710 (miles) for -1 byte.

Python 2, 63 bytes

a='\n'.join([('/'*5+'\\'*5)*6]*4);print'\n'.join([a,a[::-1]]*3)

For Python 3, do this (65 bytes):

a='\n'.join([('/'*5+'\\'*5)*6]*4);print('\n'.join([a,a[::-1]]*3))