Hypercube

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Hypercube elements E_{m,n} \!
m 0 1 2 3 4 5 6 7 8 9 10
n γn 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 γ0 0-cube Complete graph K1.svg Point
-
1                    
1 γ1 1-cube Complete graph K2.svg Line segment
{}
CDW ring.png
2 1                  
2 γ2 2-cube Kvadrato.svg Square
Tetragon
{4}
CDW ring.pngCDW 4.pngCDW dot.png
4 4 1                
3 γ3 3-cube Cube graph ortho vcenter.png Cube
Hexahedron
{4,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.png
8 12 6 1              
4 γ4 4-cube Hypercubestar.svg Tesseract
Octachoron
{4,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
16 32 24 8 1            
5 γ5 5-cube Penteract ortho petrie.svg Penteract
Decateron
{4,3,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
32 80 80 40 10 1          
6 γ6 6-cube Hexeract ortho petrie.svg Hexeract
Dodecapeton
{4,3,3,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
64 192 240 160 60 12 1        
7 γ7 7-cube Hepteract ortho petrie.svg Hepteract
Tetradeca-7-tope
{4,3,3,3,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
128 448 672 560 280 84 14 1      
8 γ8 8-cube Octeract Petrie polygon.svg Octeract
Hexadeca-8-tope
{4,3,3,3,3,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
256 1024 1792 1792 1120 448 112 16 1    
9 γ9 9-cube Enneract ortho petrie.svg Enneract
Octadeca-9-tope
{4,3,3,3,3,3,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
512 2304 4608 5376 4032 2016 672 144 18 1  
10 γ10 10-cube 10cube ortho polygon.svg Dekeract
icosa-10-tope
{4,3,3,3,3,3,3,3,3}
CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png
1024 5120 11520 15360 13440 8064 3360 960 180 20 1