Uniform 6-polytope
The E6 family
There are 39 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. Bowers-style acronym names are given for cross-referencing.

Uniform 6-polytope

Section Title: The E6 family
Table Section Text: There are 39 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. Bowers-style acronym names are given for cross-referencing.

#	Coxeter diagram	Names	Element counts

5-faces	4-faces	Cells	Faces	Edges	Vertices

139	=	122 Pentacontatetrapeton (mo)	54	702	2160	2160	720	72

140	=	Rectified 122 Rectified pentacontatetrapeton (ram)	126	1566	6480	10800	6480	720

141	=	Birectified 122 Birectified pentacontatetrapeton (barm)	126	2286	10800	19440	12960	2160

142	=	Trirectified 122 Trirectified pentacontatetrapeton (trim)	558	4608	8640	6480	2160	270

143	=	Truncated 122 Truncated pentacontatetrapeton (tim)	13680	1440

144	=	Bitruncated 122 Bitruncated pentacontatetrapeton (bitem)	6480

145	=	Tritruncated 122 Tritruncated pentacontatetrapeton (titam)	8640

146	=	Cantellated 122 Small rhombated pentacontatetrapeton (sram)	6480

147	=	Cantitruncated 122 Great rhombated pentacontatetrapeton (gram)	12960

148	=	Runcinated 122 Small prismated pentacontatetrapeton (spam)	2160

149	=	Bicantellated 122 Small birhombated pentacontatetrapeton (sabrim)	6480

150	=	Bicantitruncated 122 Great birhombated pentacontatetrapeton (gabrim)	12960

151	=	Runcitruncated 122 Prismatotruncated pentacontatetrapeton (patom)	12960

152	=	Runcicantellated 122 Prismatorhombated pentacontatetrapeton (prom)	25920

153	=	Omnitruncated 122 Great prismated pentacontatetrapeton (gopam)	51840

Sentence(s)

There are 153 uniform 6-polytopes.

final_sentence: There are 153 uniform 6-polytopes.