# How to draw this cube with holes?

I am trying to draw this cube

I tried

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{60}{120}
\begin{tikzpicture}[tdplot_main_coords,declare function={a=3;
}]
\path
(a,-a,-a) coordinate (A)
(a,a,-a) coordinate (B)
(-a,a,-a) coordinate (C)
(-a,-a,-a) coordinate (D)
(a,-a,a) coordinate (E)
(a,a,a) coordinate (F)
(-a,a,a) coordinate (G)
(-a,-a,a) coordinate (H)
(0,0,0)  coordinate (O)
;
\draw (E) -- (A) -- (B) --(C) -- (G) -- (H) -- (E) (E) -- (F) -- (G) (B) -- (F);
%\path foreach \p/\g in {A/-90,B/90,C/0,D/0,E/0,F/0,G/0,H/0}{(\p)node{}+(\g:2.5mm) node{$\p$}};
\end{tikzpicture}
\end{document}


And got

How can I get cube with holes?

• You could probably take some good advice in this question and its answer, especially the \mengersponge command you'll find there. Sep 18, 2021 at 9:02

With TikZ this is easy to draw using pics, styles and the 3d library:

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{3d}

\tikzset
{%
front face/.style={fill=gray!20,canvas is xy plane at z=1},
up    face/.style={fill=gray!50,canvas is xz plane at y=1},
east  face/.style={fill=gray!80,canvas is yz plane at x=1},
pics/square/.style={
code={\draw[fill=white,even odd rule] (0,0) rectangle (3,3) (1,1) rectangle (2,2);}},
}

\begin{document}
\begin{tikzpicture}
\foreach\i in {0,1} \foreach\s in {front face, up face, east face}
\draw[\s] (\i,1-\i) rectangle ++(1,1);
\foreach\i in {1,2} \foreach\s in {front face, up face, east face}
\draw[\s] (\i,3-\i) rectangle ++(1,1);
\pic[canvas is xy plane at z=3] {square};
\pic[canvas is xz plane at y=3] {square};
\pic[canvas is yz plane at x=3] {square};
\end{tikzpicture}
\end{document}


Update: An animated version. I shifted all the points and changed the perspective, but the rest is the same:

\documentclass     {beamer}
\usepackage        {tikz}
\usetikzlibrary    {3d,perspective}

% beamer configuration

\tikzset
{%
up face/.style={fill=gray!30,canvas is xy plane at z=-0.5},
pics/square/.style={code={\draw[fill=white,even odd rule] (-1.5,-1.5) rectangle (1.5,1.5)
(-0.5,-0.5) rectangle (0.5,0.5);}},
}

\begin{document}
\begin{frame}
\foreach\i in{1,...,18}
{
\only<\i>
{
\begin{figure}\centering
\begin{tikzpicture}[line cap=round,line join=round,isometric view,rotate around z=5*\i-45]
\pgfmathsetmacro\lc{50+2*\i} % left  color proportion
\pgfmathsetmacro\rc{86-2*\i} % right color proportion
\tikzset
{
left  face/.style={fill=gray!\lc,canvas is xz plane at y=0.5},
right face/.style={fill=gray!\rc,canvas is yz plane at x=0.5},
}
\useasboundingbox (0,0) circle (3cm);
\draw[thick,red] (0,0,-4) -- (0,0,-1.5);
\foreach\i in {0,1}
{
\draw[up    face] (0.5-\i,-0.5+\i) rectangle ++(1,1);
\draw[left  face] (0.5-\i,-0.5-\i) rectangle ++(1,1);
\draw[right face] (0.5-\i,-0.5-\i) rectangle ++(1,1);
}
\draw[thick,red] (0,0,-1.5) -- (0,0,-0.5);
\foreach\i in {0,1}
{
\draw[up    face] (-1.5+\i,-0.5-\i) rectangle ++(1,1);
\draw[left  face] (-1.5+\i,-0.5+\i) rectangle ++(1,1);
\draw[right face] (-1.5+\i,-0.5+\i) rectangle ++(1,1);
}
\draw[thick,red] (0,0,-0.5) -- (0,0,1.5);
\pic[canvas is xy plane at z= 1.5] at (0,0) {square};
\pic[canvas is xz plane at y=-1.5] at (0,0) {square};
\pic[canvas is yz plane at x=-1.5] at (0,0) {square};
\draw[thick,red] (0,0,1.5) -- (0,0,4);
\end{tikzpicture}
\end{figure}
}
}
\end{frame}
\end{document}


• A neat solution for sure! because all surfaces here are planes. Could you make the figure in different views? or better in animation? Sep 18, 2021 at 17:00
• @BlackMild, not this way, that's for sure. But, I'll think about it. Sep 18, 2021 at 17:04
• @BlackMild, I did it this way after all :-) Sep 18, 2021 at 18:05
• Very cool! So you defined isometric style of your own. Why did not you use [isometric view] or [3d view] , avaiable in Section 63.2 Setting the view of the current pgfmanual? Sep 18, 2021 at 18:13
• @BlackMild, I'm used to draw with the axes in this way. The isometric view form perspective library changes the sign in x and y axes. It's true that it's all the same for this picture, but old habits... Sep 18, 2021 at 18:46

With perspective projection and cosine lightening, in TikZ

\documentclass[border=9,tikz]{standalone}
\usepackage{tikz-3dplot}

\makeatletter
\def\camerax{0}\def\cameray{0}\def\cameraz{0}
\let\oldpointxyz\pgfpointxyz
\def\perspectivepointxyz#1#2#3{
\oldpointxyz{#1-\camerax}{#2-\cameray}{#3-\cameraz}%%% (x,y,z) is camera center
\pgfmathsetmacro\depth{\rcarot*\pgftemp@x+\rcbrot*\pgftemp@y+\rccrot*\pgftemp@z}
}
\tikzset{
at z/.code={
\pgfmathsetmacro\innerprod{\rccrot*100}\pgfkeysalso{fill=gray!\innerprod!light}
\def\pgfpointxy##1##2{\perspectivepointxyz{##1}{##2}{#1}}
},
at y/.code={
\pgfmathsetmacro\innerprod{\rcbrot*100}\pgfkeysalso{fill=ycolor!\innerprod!light}
\def\pgfpointxy##1##2{\perspectivepointxyz{##2}{#1}{##1}}
},
at x/.code={
\pgfmathsetmacro\innerprod{\rcarot*100}\pgfkeysalso{fill=xcolor!\innerprod!light}
\def\pgfpointxy##1##2{\perspectivepointxyz{#1}{##1}{##2}}
},
}
\def\face{\draw[fill=gray,even odd rule]}

\begin{document}

\foreach\leftcolor/\rightcolor in{cyan/magenta,magenta/yellow,yellow/cyan}{
\colorlet{xcolor}{\leftcolor}
\colorlet{ycolor}{\rightcolor}
\def\Nframe{45}
\foreach\frame in{1,...,\Nframe}{
\tdplotsetmaincoords{48+30*cos(360*\frame/\Nframe)}{90+90*\frame/\Nframe}
\tikz[tdplot_main_coords]{
\draw[x=1cm,y=1cm]circle(9);
\begin{scope}% inside and farther away from camera
\colorlet{light}{black}
\def\insidefarface{
(3,-9)--(-3,-9)--(-3,3)--(-9,3)--(-9,-3)--(3,-3)--(3,-9)
}
\face[at z=-3]\insidefarface;
\face[at y=-3]\insidefarface;
\face[at x=-3]\insidefarface;
\face[at y=3]\insidefarface;
\face[at x=3]\insidefarface;
\end{scope}
\begin{scope}% inside but closer to camera
\colorlet{light}{black}
\def\insidenearface{
(-3,9)--(3,9)--(3,-3)--(9,-3)--(9,3)--(-3,3)--(-3,9)
}
\face[at z=-3]\insidenearface;
\face[at y=-3]\insidenearface;
\face[at x=-3]\insidenearface;
\face[at y=3]\insidenearface;
\face[at x=3]\insidenearface;
\end{scope}
\begin{scope}% outside
\colorlet{light}{gray}
\def\outsideface{
(-9,-9)--(-9,9)--(9,9)--(9,-9)--(-9,-9)
(-3,-3)--(-3,3)--(3,3)--(3,-3)--(-3,-3)
}
\ifdim\rcbrot pt>\rcarot pt
\face[at x=9]\outsideface;
\face[at y=9]\outsideface;
\else
\face[at y=9]\outsideface;
\face[at x=9]\outsideface;
\fi
\face[at z=9]\outsideface;
\end{scope}
}
}
}

\end{document}


• +1: Amazing job Symbol 1! Sep 19, 2021 at 23:03

New solution The extrude command from graph3 of Asymptote does the job well! (see my previous answer here): figure is composed by the inner surface and the outer surface.

I will make 3D animation later! But for now you can rotate the figure by hand (drag the left mouse): download this html file and open with some browser (Microsoft Edge, Google Chrome, etc). A taste of 3D!

Top-right view

Side view

Another view

The code:

// http://asymptote.ualberta.ca/
unitsize(1cm);
//import three;
import graph3;
currentprojection=orthographic((5,1.6,1.6),zoom=.85,center=true);
pen p=yellow;

// the inner surface
draw(extrude(plane(X,Y,X+Y)),p);
draw(extrude(plane(X,Y,X+Y+3Z),-Z),p);
draw(extrude(plane(Y,Z,Y+Z),X),p);
draw(extrude(plane(Y,Z,Y+Z+3X),-X),p);
draw(extrude(plane(Z,X,Z+X),Y),p);
draw(extrude(plane(Z,X,Z+X+3Y),-Y),p);

// the outer surface
draw(extrude(plane(3X,3Y,O),Z),p);
draw(extrude(plane(3X,3Y,3Z),-Z),p);
draw(extrude(plane(3Y,3Z,O),X),p);
draw(extrude(plane(3Y,3Z,3X),-X),p);
draw(extrude(plane(3Z,3X,O),Y),p);
draw(extrude(plane(3Z,3X,3Y),-Y),p);


Old solution I guess that you expect answers with other tools. Also @SebGlav cited a nice link. So here is my rough solution with Asymptote for comparison. My computer has weak graphic card, the display of color of the figure is a bit incorrect.

Some improvements on light are needed to make the figure more clearly. At least, the edges can be drawn. If anyone has suggestion of improvement with Asymptote, I am all ears.

// http://asymptote.ualberta.ca/
unitsize(1cm);
import three;
currentprojection=orthographic((1,.5,.4),zoom=.85,center=true);

pen p=white;
draw(xscale3(3)*shift(0,1,1)*unitcube,p);
draw(yscale3(3)*shift(1,0,1)*unitcube,p);
draw(zscale3(3)*shift(1,1,0)*unitcube,p);

draw(scale3(3)*unitcube,yellow+opacity(.5));

• Update: for now you can rotate the figure by hand (drag the left mouse): download this html file dropbox.com/s/y05aa4g2nblnpa4/CubeWithHoles.html and open with some browser (Microsoft Edge, Google Chrome, etc). A taste of 3D! Sep 19, 2021 at 4:02

Compile with Asymptote.

Note that the problem of opacity is still not implemented in Asymptote at present.

Compile at http://asymptote.ualberta.ca/

Specially, if you have a powerful computer, you will learn 3D Asymptote easily, otherwise you will get a common error in Asymptote is out of memory, :-). Sob!

// settings.render=10;
size(8cm);
import three;
currentprojection=orthographic((1,0.5,0.35));
currentlight=nolight;
// See three.asy
// Line 2012: restricted path3 unitsquare3=O--X--X+Y--Y--cycle;
path3 p1=unitsquare3;
path3 p2=shift(1/3*(X+Y))*scale3(1/3)*p1;

// transform3 t=scale(1.25,1,1);

surface s=surface(reverse(p1)^^p2,planar=true);
surface[] S={s,rotate(90,O,X)*s,rotate(-90,O,Y)*s
,shift(Z)*s,rotate(90,X,X+Y)*s,rotate(-90,Y,X+Y)*s};
path3[] p3=p1^^p2;
path3[][] P={p3,rotate(90,O,X)*p3,rotate(-90,O,Y)*p3
,shift(Z)*p3,rotate(90,X,X+Y)*p3,rotate(-90,Y,X+Y)*p3};
draw(S,white);
for (int i=0; i<P.length; ++i){
draw(P[i][0],0.8bp+red);
draw(P[i][1],0.8bp+blue);
}

surface s0=scale3(1/3)*unitcube;
transform3[] T={identity4,shift(1/3*X),shift(2/3*X)
,shift(1/3*Y),shift(2/3*Y),shift(1/3*X+2/3*Y)
,shift(2/3*X+1/3*Y),shift(2/3*(X+Y))};
for (transform3 i : T) draw(i*s0,white);
for (transform3 i : T) draw(shift(2/3*Z)*i*s0,white);

transform3 tt(real r)
{
return rotate(r,1/2*(X+Y),1/2*(X+Y)+(0,0,1));
}

for (int i : new int[]{0,90,180,270})
{
draw(tt(i)*shift(1/3*Z)*s0,white);
}

draw(shift(1/3*(X+Y))*scale(1/3,1/3,1)*unitcube,invisible,0.8bp+blue);
draw(shift(1/3*(Z+Y))*scale(1,1/3,1/3)*unitcube,invisible,0.8bp+blue);
draw(shift(1/3*(X+Z))*scale(1/3,1,1/3)*unitcube,invisible,0.8bp+blue);


Animation:

import three;
import graph3;
currentprojection=orthographic((1,0.5,0.35));
currentlight=nolight;

size(8cm,0);
string[] files;
int numberofframes=72;
for (int i=0; i <= numberofframes; ++i)
{
files[i]="T"+(string) i;
picture pic;
// See three.asy
// Line 2012: restricted path3 unitsquare3=O--X--X+Y--Y--cycle;
path3 p1=unitsquare3;
path3 p2=shift(1/3*(X+Y))*scale3(1/3)*p1;

transform3 t=rotate(i*5,Z);

surface s=surface(reverse(p1)^^p2,planar=true);
surface[] S={s,rotate(90,O,X)*s,rotate(-90,O,Y)*s
,shift(Z)*s,rotate(90,X,X+Y)*s,rotate(-90,Y,X+Y)*s};
path3[] p3=p1^^p2;
path3[][] P={p3,rotate(90,O,X)*p3,rotate(-90,O,Y)*p3
,shift(Z)*p3,rotate(90,X,X+Y)*p3,rotate(-90,Y,X+Y)*p3};

draw(pic,t*S,white);
for (int i=0; i<P.length; ++i){
draw(pic,t*P[i][0],0.8bp+red);
draw(pic,t*P[i][1],0.8bp+blue);
}

surface s0=scale3(1/3)*unitcube;
transform3[] T={identity4,shift(1/3*X),shift(2/3*X)
,shift(1/3*Y),shift(2/3*Y),shift(1/3*X+2/3*Y)
,shift(2/3*X+1/3*Y),shift(2/3*(X+Y))};
for (transform3 i : T) draw(pic,t*i*s0,white);
for (transform3 i : T) draw(pic,t*shift(2/3*Z)*i*s0,white);

transform3 tt(real r)
{
return rotate(r,1/2*(X+Y),1/2*(X+Y)+(0,0,1));
}

for (int i : new int[]{0,90,180,270})
{
draw(pic,t*tt(i)*shift(1/3*Z)*s0,white);
}

draw(pic,t*shift(1/3*(X+Y))*scale(1/3,1/3,1)*unitcube,invisible,0.8bp+blue);
draw(pic,t*shift(1/3*(Z+Y))*scale(1,1/3,1/3)*unitcube,invisible,0.8bp+blue);
draw(pic,t*shift(1/3*(X+Z))*scale(1/3,1,1/3)*unitcube,invisible,0.8bp+blue);

xaxis3(pic,"$x$",-.5,2,Arrow3);
yaxis3(pic,"$y$",-2,2,Arrow3);
zaxis3(pic,"$z$",-.5,2,Arrow3);