Template:Symmetry groups
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| rank | Simplex | Orthoplex/Hypercube | Demicube | Gosset | Icositetrachoric | Pentagonal | Polygonal |
|---|---|---|---|---|---|---|---|
| n | An | Bn | Dn | En | F4 | Hn | I2(p) |
| 2 | triangle   
|
square 
|
pentagon  
|
heptagon (p = 7) 
| |||
| 3 | tetrahedron
|
octahedron
|
tetrahedron 
|
icosahedron
|
|||
| 4 | pentachoron
|
hexadecachoron
|
hexadecachoron
|
rectified pentachoron    
|
icositetrachoron
|
hexacosichoron
|
|
| 5 | 5-simplex
|
5-orthoplex
|
5-demicube
|
5-demicube
|
|||
| 6 | 6-simplex
|
6-orthoplex
|
6-demicube
|
27-72-peton
|
|||
| 7 | 7-simplex
|
7-orthoplex
|
7-demicube
|
126-576-exon
|
|||
| 8 | 8-simplex
|
8-orthoplex
|
8-demicube
|
2160-17280-zetton
|
|||
| 9 | 9-simplex
|
9-orthoplex
|
9-demicube
|
||||
| n | n-simplex | n-hypercube | n-demicube | (n-4)2,1 polytope |