Hypercube

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Hypercube elements
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 Point
-
1                    
1 γ1 1-cube Line segment
{}
2 1                  
2 γ2 2-cube Square
Tetragon
{4}
4 4 1                
3 γ3 3-cube Cube
Hexahedron
{4,3}
8 12 6 1              
4 γ4 4-cube Tesseract
Octachoron
{4,3,3}
16 32 24 8 1            
5 γ5 5-cube Penteract
Decateron
{4,3,3,3}
32 80 80 40 10 1          
6 γ6 6-cube Hexeract
Dodecapeton
{4,3,3,3,3}
64 192 240 160 60 12 1        
7 γ7 7-cube Hepteract
Tetradeca-7-tope
{4,3,3,3,3,3}
128 448 672 560 280 84 14 1      
8 γ8 8-cube Octeract
Hexadeca-8-tope
{4,3,3,3,3,3,3}
256 1024 1792 1792 1120 448 112 16 1    
9 γ9 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 γ10 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