| Acronym | pentaspan, pent || span |
| Name | (degenerate) pent atop span |
| Circumradius | ∞ i.e. flat in euclidean space |
| Face vector | 352, 1840, 3680, 3440, 1452, 204 |
| Confer |
|
It either can be thought of as a degenerate 6D segmentotope with zero height, or as a 5D euclidean decomposition of the larger base into smaller bits.
Incidence matrix according to Dynkin symbol
oo3ox3oo3oo4xx&#x → height = 0
(pent || span)
o.3o.3o.3o.4o. | 32 * | 5 10 0 0 | 10 30 30 0 0 0 0 | 10 10 20 60 30 0 0 0 0 0 0 | 5 5 20 5 20 30 10 0 0 0 0 | 1 1 5 10 5 0
.o3.o3.o3.o4.o | * 320 | 0 1 6 3 | 0 6 3 3 6 12 3 | 0 3 6 12 3 3 6 2 6 6 1 | 0 3 6 2 6 6 1 1 3 3 2 | 0 1 3 3 2 1
------------------+--------+----------------+----------------------------+-------------------------------------------+---------------------------------------+----------------
.. .. .. .. x. | 2 0 | 80 * * * | 4 0 6 0 0 0 0 | 6 0 0 12 12 0 0 0 0 0 0 | 4 0 4 0 4 12 6 0 0 0 0 | 1 0 1 4 4 0
oo3oo3oo3oo4oo&#x | 1 1 | * 320 * * | 0 6 3 0 0 0 0 | 0 3 6 12 3 0 0 0 0 0 0 | 0 3 6 2 6 6 1 0 0 0 0 | 0 1 3 3 2 0
.. .x .. .. .. | 0 2 | * * 960 * | 0 1 0 1 2 2 0 | 0 1 2 2 0 2 2 1 2 1 0 | 0 2 2 1 2 1 0 1 2 1 1 | 0 1 2 1 1 1
.. .. .. .. .x | 0 2 | * * * 480 | 0 0 1 0 0 4 2 | 0 0 0 4 2 0 2 0 2 4 1 | 0 0 2 0 2 4 1 0 1 2 2 | 0 0 1 2 2 1
------------------+--------+----------------+----------------------------+-------------------------------------------+---------------------------------------+----------------
.. .. .. o.4x. | 4 0 | 4 0 0 0 | 80 * * * * * * | 3 0 0 0 3 0 0 0 0 0 0 | 3 0 0 0 0 3 3 0 0 0 0 | 1 0 0 1 3 0
.. ox .. .. ..&#x | 1 2 | 0 2 1 0 | * 960 * * * * * | 0 1 2 2 0 0 0 0 0 0 0 | 0 2 2 1 2 1 0 0 0 0 0 | 0 1 2 1 1 0
.. .. .. .. xx&#x | 2 2 | 1 2 0 1 | * * 480 * * * * | 0 0 0 4 2 0 0 0 0 0 0 | 0 0 2 0 2 4 1 0 0 0 0 | 0 0 1 2 2 0
.o3.x .. .. .. | 0 3 | 0 0 3 0 | * * * 320 * * * | 0 1 0 0 0 2 2 0 0 0 0 | 0 2 2 0 0 0 0 1 2 1 0 | 0 1 2 1 0 1
.. .x3.o .. .. | 0 3 | 0 0 3 0 | * * * * 640 * * | 0 0 1 0 0 1 0 1 1 0 0 | 0 1 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
.. .x .. .. .x | 0 4 | 0 0 2 2 | * * * * * 960 * | 0 0 0 1 0 0 1 0 1 1 0 | 0 0 1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
.. .. .. .o4.x | 0 4 | 0 0 0 4 | * * * * * * 240 | 0 0 0 0 1 0 0 0 0 2 1 | 0 0 0 0 0 2 1 0 0 1 2 | 0 0 0 1 2 1
------------------+--------+----------------+----------------------------+-------------------------------------------+---------------------------------------+----------------
.. .. o.3o.4x. ♦ 8 0 | 12 0 0 0 | 6 0 0 0 0 0 0 | 40 * * * * * * * * * * | 2 0 0 0 0 0 1 0 0 0 0 | 1 0 0 0 2 0
oo3ox .. .. ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 0 0 | * 320 * * * * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.. ox3oo .. ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 0 1 0 0 | * * 640 * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
.. ox .. .. xx&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 0 1 0 | * * * 960 * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.. .. .. oo4xx&#x ♦ 4 4 | 4 4 0 4 | 1 0 4 0 0 0 1 | * * * * 240 * * * * * * | 0 0 0 0 0 2 1 0 0 0 0 | 0 0 0 1 2 0
.o3.x3.o .. .. ♦ 0 6 | 0 0 12 0 | 0 0 0 4 4 0 0 | * * * * * 160 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.o3.x .. .. .x ♦ 0 6 | 0 0 6 3 | 0 0 0 2 0 3 0 | * * * * * * 320 * * * * | 0 0 1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
.. .x3.o3.o .. ♦ 0 4 | 0 0 6 0 | 0 0 0 0 4 0 0 | * * * * * * * 160 * * * | 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
.. .x3.o .. .x ♦ 0 6 | 0 0 6 3 | 0 0 0 0 2 3 0 | * * * * * * * * 320 * * | 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
.. .x .. .o4.x ♦ 0 8 | 0 0 4 8 | 0 0 0 0 0 4 2 | * * * * * * * * * 240 * | 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
.. .. .o3.o4.x ♦ 0 8 | 0 0 0 12 | 0 0 0 0 0 0 6 | * * * * * * * * * * 40 | 0 0 0 0 0 0 1 0 0 0 2 | 0 0 0 0 2 1
------------------+--------+----------------+----------------------------+-------------------------------------------+---------------------------------------+----------------
.. o.3o.3o.4x. ♦ 16 0 | 32 0 0 0 | 24 0 0 0 0 0 0 | 8 0 0 0 0 0 0 0 0 0 0 | 10 * * * * * * * * * * | 1 0 0 0 1 0
oo3ox3oo .. ..&#x ♦ 1 6 | 0 6 12 0 | 0 12 0 4 4 0 0 | 0 4 4 0 0 1 0 0 0 0 0 | * 160 * * * * * * * * * | 0 1 1 0 0 0
oo3ox .. .. xx&#x ♦ 2 6 | 1 6 6 3 | 0 6 3 2 0 3 0 | 0 2 0 3 0 0 1 0 0 0 0 | * * 320 * * * * * * * * | 0 0 1 1 0 0
.. ox3oo3oo ..&#x ♦ 1 4 | 0 4 6 0 | 0 6 0 0 4 0 0 | 0 0 4 0 0 0 0 1 0 0 0 | * * * 160 * * * * * * * | 0 1 0 0 1 0
.. ox3oo .. xx&#x ♦ 2 6 | 1 6 6 3 | 0 6 3 0 2 3 0 | 0 0 2 3 0 0 0 0 1 0 0 | * * * * 320 * * * * * * | 0 0 1 0 1 0
.. ox .. oo4xx&#x ♦ 4 8 | 4 8 4 8 | 1 4 8 0 0 4 2 | 0 0 0 4 2 0 0 0 0 1 0 | * * * * * 240 * * * * * | 0 0 0 1 1 0
.. .. oo3oo4xx&#x ♦ 8 8 | 12 8 0 12 | 6 0 12 0 0 0 6 | 1 0 0 0 6 0 0 0 0 0 1 | * * * * * * 40 * * * * | 0 0 0 0 2 0
.o3.x3.o3.o .. ♦ 0 10 | 0 0 30 0 | 0 0 0 10 20 0 0 | 0 0 0 0 0 5 0 5 0 0 0 | * * * * * * * 32 * * * | 0 1 0 0 0 1
.o3.x3.o .. .x ♦ 0 12 | 0 0 24 6 | 0 0 0 8 8 12 0 | 0 0 0 0 0 2 4 0 4 0 0 | * * * * * * * * 80 * * | 0 0 1 0 0 1
.o3.x .. .o4.x ♦ 0 12 | 0 0 12 12 | 0 0 0 4 0 12 3 | 0 0 0 0 0 0 4 0 0 3 0 | * * * * * * * * * 80 * | 0 0 0 1 0 1
.. .x3.o3.o4.x ♦ 0 64 | 0 0 96 96 | 0 0 0 0 64 96 48 | 0 0 0 0 0 0 0 16 32 24 8 | * * * * * * * * * * 10 | 0 0 0 0 1 1
------------------+--------+----------------+----------------------------+-------------------------------------------+---------------------------------------+----------------
o.3o.3o.3o.4x. ♦ 32 0 | 80 0 0 0 | 80 0 0 0 0 0 0 | 40 0 0 0 0 0 0 0 0 0 0 | 10 0 0 0 0 0 0 0 0 0 0 | 1 * * * * *
oo3ox3oo3oo ..&#x ♦ 1 10 | 0 10 30 0 | 0 30 0 10 20 0 0 | 0 10 20 0 0 5 0 5 0 0 0 | 0 5 0 5 0 0 0 1 0 0 0 | * 32 * * * *
oo3ox3oo .. xx&#x ♦ 2 12 | 1 12 24 6 | 0 24 6 8 8 12 0 | 0 8 8 12 0 2 4 0 4 0 0 | 0 2 4 0 4 0 0 0 1 0 0 | * * 80 * * *
oo3ox .. oo4xx&#x ♦ 4 12 | 4 12 12 12 | 1 12 12 4 0 12 3 | 0 4 0 12 3 0 4 0 0 3 0 | 0 0 4 0 0 3 0 0 0 1 0 | * * * 80 * *
.. ox3oo3oo4xx&#x ♦ 16 64 | 32 64 96 96 | 24 96 96 0 64 96 48 | 8 0 64 96 48 0 0 16 32 24 8 | 1 0 0 16 32 24 8 0 0 0 1 | * * * * 10 *
.o3.o3.o3.o4.o ♦ 0 320 | 0 0 960 480 | 0 0 0 320 640 960 240 | 0 0 0 0 0 160 320 160 320 240 40 | 0 0 0 0 0 0 0 32 80 80 10 | * * * * * 1
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