Acronym | pautpen |
Name | penta-augmentated truncated pentachoron |
Circumradius | ... |
Dihedral angles |
|
Face vector | 50, 160, 160, 50 |
Confer |
Note that the A-sized edges would still survive the notational hull operation, but here are assumed to not contribute. Thus the underlying orthogonal hexagons provide non-convex dihedral angles. Nonetheless, this polychoron has the strange property that it's entire surface is exposed, even though it is not convex, that is, it's a non-self-intersecting concave polychoron.
Incidence matrix according to Dynkin symbol
xo3xx3oo3oA&#zx → height = 0, where A = 3/2 o.3o.3o.3o. | 20 * | 1 3 3 0 | 3 3 3 6 0 0 | 1 6 3 0 .o3.o3.o3.o | * 30 | 0 0 2 4 | 0 0 1 4 2 2 | 0 2 2 1 ---------------+-------+-------------+-------------------+---------- x. .. .. .. | 2 0 | 10 * * * | 3 0 3 0 0 0 | 0 6 0 0 .. x. .. .. | 2 0 | * 30 * * | 1 2 0 2 0 0 | 1 2 2 0 oo3oo3oo3oo&#x | 1 1 | * * 60 * | 0 0 1 2 0 0 | 0 2 1 0 .. .x .. .. | 0 2 | * * * 60 | 0 0 0 1 1 1 | 0 1 1 1 ---------------+-------+-------------+-------------------+---------- x.3x. .. .. | 6 0 | 3 3 0 0 | 10 * * * * * | 0 2 0 0 .. x.3o. .. | 3 0 | 0 3 0 0 | * 20 * * * * | 1 0 1 0 xo .. .. ..&#x | 2 1 | 1 0 2 0 | * * 30 * * * | 0 2 0 0 .. xx .. ..&#x | 2 2 | 0 1 2 1 | * * * 60 * * | 0 1 1 0 .o3.x .. .. | 0 3 | 0 0 0 3 | * * * * 20 * | 0 1 0 1 .. .x3.o .. | 0 3 | 0 0 0 3 | * * * * * 20 | 0 0 1 1 ---------------+-------+-------------+-------------------+---------- .. x.3o.3o. ♦ 4 0 | 0 6 0 0 | 0 4 0 0 0 0 | 5 * * * xo3xx .. ..&#x ♦ 6 3 | 3 3 6 3 | 1 0 3 3 1 0 | * 20 * * .. xx3oo ..&#x ♦ 3 3 | 0 3 3 3 | 0 1 0 3 0 1 | * * 20 * .o3.x3.o .. ♦ 0 6 | 0 0 0 12 | 0 0 0 0 4 4 | * * * 5
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