Polytope families

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There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality. These are tabulated here with Petrie polygon projection graphs and Coxeter–Dynkin diagrams.

Table of irreducible polytope families
Family n	n-simplex	n-hypercube	n-orthoplex	n-demicube	1k2	2k1	k21	pentagonal polytope
Group	An	Bn		I2(p) Dn	E6 E7 E8 F4 G2			Hn
2	Triangle	Square		p-gon (example: p=7)	Hexagon			Pentagon
3	Tetrahedron	Cube	Octahedron	Tetrahedron				Dodecahedron	Icosahedron
4	5-cell	Tesseract	16-cell	Demitesseract	24-cell			120-cell	600-cell
5	5-simplex	5-cube	5-orthoplex	5-demicube
6	6-simplex	6-cube	6-orthoplex	6-demicube	122	221
7	7-simplex	7-cube	7-orthoplex	7-demicube	132	231	321
8	8-simplex	8-cube	8-orthoplex	8-demicube	142	241	421
9	9-simplex	9-cube	9-orthoplex	9-demicube
10	10-simplex	10-cube	10-orthoplex	10-demicube