Talk:Pentagonal polytope

another series

There's another interesting dimensional series of polytopes: {3,4} octahedron/cube/snub cube, {3,4,3} 24-cell/snub 24-cell, {3,4,3,3} 24-cell honeycomb/16-cell honeycomb/snub 24-cell honeycomb in Euclidean 4-space, and {3,4,3,3,3} noncompact honeycomb(s) in hyperbolic 5-space. Tom Ruen (talk) 01:32, 24 November 2011 (UTC)

I think this is the F_n family of polytopes. I would create an article on that, but I'm not sure what would be a good title. Double sharp (talk) 14:28, 11 January 2012 (UTC)

We might also have an article for the G_n family (which - I think - contains {6}, {6, 3}, {6, 3, 3}, etc.) Double sharp (talk) 14:33, 11 January 2012 (UTC)

Let's see what we have: Tom Ruen (talk) 16:32, 4 February 2012 (UTC)

G family polytope: S₁, E₂, H₃

• Regular 1: {6}, {6,3}, {6,3,3}
• Truncated 1: t₁{6}, t₁{6,3}, t₁{6,3,3}
• Truncated 2: t₁{6}, t₁{3,6}, t₁{3,3,6}
• Regular 2: {6}, {3,6}, {3,3,6}
• Omnitruncatd: o{6}, o{6,3}, o{6,3,3}
• Snub: s{6}, s{6,3}, s{6,3,3}

F family polytope: S₂, S₃, E₄, H₅

• Regular 1: {3,4}, {3,4,3}, {3,4,3,3}, {3,4,3,3,3}
• Truncated 1: t{3,4}, t{3,4,3}, t{3,4,3,3}, t{3,4,3,3,3}
• Rectified 1: t₁{4,3}, t₁{3,4,3}, t₁{3,3,4,3}, t₁{3,3,3,4,3}
• Rectified 2: t₁{4,3}, t₁{3,4,3}, t₁{3,3,4,3}, t₁{3,3,3,4,3}
• Truncated 2: t{4,3}, t{3,4,3}, {3,3,4,3}, t{3,3,3,4,3}
• Regular 2: {4,3}, {3,4,3}, {3,3,4,3}, {3,3,3,4,3}
• Cantellated: t_0,2{3,4}, t_0,2{3,4,3}, t_0,2{3,4,3,3}, t_0,2{3,4,3,3,3}
• Cantitruncated: t_0,1,2{3,4}, t_0,1,2{3,4,3}, t_0,1,2{3,4,3,3}, t_0,1,2{3,4,3,3,3}
• Omnitruncated: o{3,4}, o{3,4,3}, o{3,4,3,3}, o{3,4,3,3,3}
• Snub s{3,4}, s{3,4,3}, s{3,4,3,3}, s{3,4,3,3,3}

Projections

I wonder how this could be included? Tom Ruen (talk) 00:48, 9 May 2013 (UTC)

Pentagon	Icosahedron	Dodecahedron	600-cell	120-cell
V:5	V:12	V:20	V:120	V:600
$H_{2}$	$H_{3}$		$H_{4}$
$A_{4}$	$D_{6}$		$E_{8}$
5-cell	311	131	421	142
V:5	V:12	V:32	V:240	V:17280