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Hypercube
convex polytope, the n-dimensional analogue of a square and a cube
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Hypercube elements
E
m
,
n
{\displaystyle E_{m,n}\!}
m
0
1
2
3
4
5
6
7
8
9
10
n
γ
n
n-cube
Petrie polygon projection
Names
Schläfli symbol
Coxeter-Dynkin
Vertices
Edges
Faces
Cells
4
-faces
5
-faces
6
-faces
7
-faces
8
-faces
9
-faces
10
-faces
0
γ
0
0-cube
Point
-
1
1
γ
1
1-cube
Line segment
{}
2
1
2
γ
2
2-cube
Square
Tetragon
{4}
4
4
1
3
γ
3
3-cube
Cube
Hexahedron
{4,3}
8
12
6
1
4
γ
4
4-cube
Tesseract
Octachoron
{4,3,3}
16
32
24
8
1
5
γ
5
5-cube
Penteract
Decateron
{4,3,3,3}
32
80
80
40
10
1
6
γ
6
6-cube
Hexeract
Dodecapeton
{4,3,3,3,3}
64
192
240
160
60
12
1
7
γ
7
7-cube
Hepteract
Tetradeca-7-tope
{4,3,3,3,3,3}
128
448
672
560
280
84
14
1
8
γ
8
8-cube
Octeract
Hexadeca-8-tope
{4,3,3,3,3,3,3}
256
1024
1792
1792
1120
448
112
16
1
9
γ
9
9-cube
Enneract
Octadeca-9-tope
{4,3,3,3,3,3,3,3}
512
2304
4608
5376
4032
2016
672
144
18
1
10
γ
10
10-cube
Dekeract
icosa-10-tope
{4,3,3,3,3,3,3,3,3}
1024
5120
11520
15360
13440
8064
3360
960
180
20
1