Question

How to specify the position of an object moving in the space? Using four dimensions.

Answer 1

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.

Tesseract

8-cell

4-cube

Schlegel wireframe 8-cell.png

Schlegel diagram

Type

Convex regular 4-polytope

Schläfli symbol

{4,3,3}

t0,3{4,3,2} or {4,3}×{ }

t0,2{4,2,4} or {4}×{4}

t0,2,3{4,2,2} or {4}×{ }×{ }

t0,1,2,3{2,2,2} or { }×{ }×{ }×{ }

Coxeter diagram

CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png

CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png

CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.png

CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node 1.png

CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 2.pngCDel node 1.png

Cells

8 {4,3} Hexahedron.png

Faces

24 {4}

Edges

32

Vertices

16

Vertex figure

8-cell verf.png

Tetrahedron

Petrie polygon

octagon

Coxeter group

B4, [3,3,4]

Dual

16-cell

Properties

convex, isogonal, isotoxal, isohedral

Uniform index

10