Tesseract (Hypercube) Viewer

See a tesseract, the four-dimensional cube, also called a 4-cube or hypercube. It has 16 corners, 32 edges, 24 square faces and 8 cubes as its cells. We cannot see four dimensions, so the tool turns it in 4D and then projects it: first to 3D, with a camera on the fourth axis (perspective) or by dropping that axis (orthographic), then onto the page. Turn it in any of the six planes it can rotate in (xy, xz, xw, yz, yw, zw) and press Spin to watch a turn in one of them. With no turn and the camera just outside, you get the familiar cube inside a cube. Edges are coloured by the direction they run in, so you can follow the fourth direction. Change the dimensions from 2 to 6 to compare the square, the cube, the tesseract and the 5- and 6-cubes. It prints on US Letter or A4, filling the page or at a width and height you type. Download a PDF, a 300 DPI PNG, an SVG or a PNG of the view. Nothing is uploaded.

100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.

How to view and print a tesseract

1. Pick a preset, or set the number of dimensions (4 for a tesseract).
2. Turn it in the six planes, and choose which plane Spin turns it in.
3. Choose perspective or orthographic for 4D to 3D and for 3D to the page.
4. Set the turn and the tilt of the 3D view; press Spin.
5. Choose edge colours, line width, corner dots and the size.
6. Download the PDF and print at 100% (Actual size), or the PNG, SVG or view PNG.

What you can use it for

• Maths lessons on dimensions, hypercubes and counting faces
• Posters and prints of a 4D cube
• Slides on rotation and projection
• Pen plotter and laser art from the SVG
• Comparing the square, cube, tesseract, 5-cube and 6-cube
• Reference drawings for wire or 3D-printed models

Corners, edges and faces of n-cubes

Shape	Dimensions	Corners (2^n)	Edges (n × 2^(n − 1))	Squares	Cubes	Cells (2n)
Square (2-cube)	2	4	4	1	–	–
Cube (3-cube)	3	8	12	6	1	–
Tesseract (4-cube)	4	16	32	24	8	8
5-cube (penteract)	5	32	80	80	40	10
6-cube (hexeract)	6	64	192	240	160	12

Counted by the tool by listing every face, and equal to 2^(n − m) × C(n, m) for every n and m shown (tested). Formulas from Wikipedia’s Hypercube page; the tesseract’s 16, 32, 24 and 8 from its Tesseract page (both read 13 November 2026).

The 13 presets

Preset	Dimensions	4D to 3D	3D to the page	Turned in	Edges drawn	Determinant of the turn
Tesseract: cube in a cube (cell-first perspective)	4	perspective, d = 2	orthographic	none	32	1.000000000
Tesseract turned in xw and yw	4	perspective, d = 3	perspective, e = 7	xw 30°, yw 20°	32	1.000000000
Tesseract, orthographic, turned in four planes	4	orthographic	orthographic	xy 15°, xw 35°, yw 25°, zw 20°	32	1.000000000
Tesseract seen straight along w: a cube	4	orthographic	orthographic	none	32	1.000000000
Tesseract, corner towards you	4	perspective, d = 3.5	perspective, e = 7	xw 45°, yw 35°, zw 30°	32	1.000000000
Tesseract in one colour	4	perspective, d = 3	perspective, e = 7	xw 30°, yw 20°	32	1.000000000
Thin lines for a pen plotter	4	perspective, d = 3	orthographic	xw 30°, yw 20°	32	1.000000000
Tesseract on a dark page	4	perspective, d = 3	perspective, e = 7	xw 25°, zw 30°	32	1.000000000
2-cube: the square	2	–	orthographic	none	4	1.000000000
3-cube: the cube	3	–	perspective, e = 6	xy 20°, yz 15°	12	1.000000000
5-cube (penteract)	5	orthographic	orthographic	xw 30°, yw 20° (+ fixed turns for the extra axes)	80	1.000000000
6-cube (hexeract)	6	orthographic	orthographic	xw 30°, yw 20° (+ fixed turns for the extra axes)	192	1.000000000
Real size: tesseract in a 150 mm square	4	perspective, d = 3	perspective, e = 7	xw 30°, yw 20°	32	1.000000000

Worked out by the tool on US Letter.

Perspective: near cell against far cell

4D camera distance d	Scale of the near cell d / (d − 1)	Scale of the far cell d / (d + 1)	Near ÷ far
1.5	3.0000	0.6000	5.0000
2	2.0000	0.6667	3.0000
3	1.5000	0.7500	2.0000
5	1.2500	0.8333	1.5000
10	1.1111	0.9091	1.2222

Worked out by the tool for the tesseract with corners at ±1 and no turn: a corner with w = 1 is scaled by d / (d − 1), one with w = −1 by d / (d + 1).

What prints

Download	What is in it
PDF	The edges at the line width you set, coloured by direction or in one colour, with corner dots if set, the counts and the view in the footer and a check bar
PNG 300 DPI	The same sheet as a picture
SVG	The same edges and dots
View PNG	The view as set, 1600 × 1600 pixels

For a plotter or cutter, use SVG to DXF; for paper models of ordinary cubes and solids, Shape Nets.

Which tool to use

You want	Use
A tesseract or any 2- to 6-cube, turned and projected	Tesseract (Hypercube) Viewer (this page)
Nets to fold real cubes and prisms	Shape Nets
Repeating cube patterns	Cube Pattern
Metatron’s cube	Metatron’s Cube

Other tools: the Op Art Generator for line illusions, and the String Art Generator for straight-line art.

Frequently asked questions

What is a tesseract?

The four-dimensional version of a cube, also called a 4-cube or hypercube. A square is bounded by 4 edges and a cube by 6 squares; a tesseract is bounded by 8 cubes, meeting at right angles.

How many corners, edges and faces does a tesseract have?

16 corners, 32 edges, 24 square faces and 8 cubes. The tool counts them by listing them, and the table compares the counts with the formula.

Is there a formula for any number of dimensions?

Yes. An n-dimensional cube has 2^n corners, n × 2^(n − 1) edges and, in general, 2^(n − m) × C(n, m) faces of dimension m, where C(n, m) is the number of ways to choose m of the n directions. For n = 4 that gives 16, 32, 24 and 8.

How do you rotate something in 4D?

In any dimension a rotation turns one flat plane of two directions and leaves the others alone. Four directions give six such planes: xy, xz, xw, yz, yw and zw. The tool has a slider for each and multiplies the six turns together; every result is checked to keep lengths and right angles (determinant 1).

Why does it turn inside out when it spins?

A turn in a plane that includes w, the fourth direction, moves corners towards and away from the 4D camera. In perspective the nearer cube looks bigger and the farther one smaller, so the cubes seem to pass through each other while every edge keeps the same real length.

What is the cube in a cube?

The view with no 4D turn and the camera on the w axis just outside the shape. The cell nearest the camera projects to the big outer cube and the farthest to the small inner one; the other six cells become the six squashed shapes between them. This is like a Schlegel diagram.

Perspective or orthographic?

Perspective divides by the distance to the camera, so far parts look smaller. Orthographic just drops the extra direction, so parallel edges stay parallel and many corners can land on top of each other. Try both: the table shows how much bigger the near cell looks than the far one.

What about 5 and 6 dimensions?

Set the dimensions to 5 or 6. The 5-cube has 32 corners and 80 edges, the 6-cube 64 corners and 192 edges. Their extra directions get fixed turns so they do not hide behind the others.

Where does the word tesseract come from?

The Oxford English Dictionary traces it to Charles Howard Hinton’s 1888 book A New Era of Thought. It comes from the Greek for four and ray, for the four edges at each corner.

Is it free?

Yes. There is no sign-up, no watermark and no limit.

Is anything uploaded?

No. Every point, face, corner and edge is worked out by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.