| Acronym | zeep |
| Name |
hecatonicosoctaexon prism, vertex figure of riv |
| Circumradius | sqrt(3)/2 = 0.866025 |
| Coordinates | (1/sqrt(2), 0, 0, 0, 0, 0, 0, 1/2) & all permutations in all but last coord., all changes of sign |
| Volume | sqrt(2)/630 = 0.0022448 |
| Face vector | 28, 182, 644, 1400, 1904, 1568, 704, 130 |
| Confer |
|
Incidence matrix according to Dynkin symbol
x x3o3o3o3o3o4o . . . . . . . . | 28 | 1 12 | 12 60 | 60 160 | 160 240 | 240 192 | 192 64 | 64 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x . . . . . . . | 2 | 14 * ♦ 12 0 | 60 0 | 160 0 | 240 0 | 192 0 | 64 0 . x . . . . . . | 2 | * 168 | 1 10 | 10 40 | 40 80 | 80 80 | 80 32 | 32 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x x . . . . . . | 4 | 2 2 | 84 * ♦ 10 0 | 40 0 | 80 0 | 80 0 | 32 0 . x3o . . . . . | 3 | 0 3 | * 560 | 1 8 | 8 24 | 24 32 | 32 16 | 16 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x x3o . . . . . ♦ 6 | 3 6 | 3 2 | 280 * ♦ 8 0 | 24 0 | 32 0 | 16 0 . x3o3o . . . . ♦ 4 | 0 6 | 0 4 | * 1120 | 1 6 | 6 12 | 12 8 | 8 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x x3o3o . . . . ♦ 8 | 4 12 | 6 8 | 4 2 | 560 * ♦ 6 0 | 12 0 | 8 0 . x3o3o3o . . . ♦ 5 | 0 10 | 0 10 | 0 5 | * 1344 | 1 4 | 4 4 | 4 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x x3o3o3o . . . ♦ 10 | 5 20 | 10 20 | 10 10 | 5 2 | 672 * | 4 0 | 4 0 . x3o3o3o3o . . ♦ 6 | 0 15 | 0 20 | 0 15 | 0 6 | * 896 | 1 2 | 2 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x x3o3o3o3o . . ♦ 12 | 6 30 | 15 40 | 20 30 | 15 12 | 6 2 | 448 * | 2 0 . x3o3o3o3o3o . ♦ 7 | 0 21 | 0 35 | 0 35 | 0 21 | 0 7 | * 256 | 1 1 ----------------+----+--------+--------+----------+----------+---------+---------+------ x x3o3o3o3o3o . ♦ 14 | 7 42 | 21 70 | 35 70 | 35 42 | 21 14 | 7 2 | 128 * . x3o3o3o3o3o4o ♦ 14 | 0 84 | 0 280 | 0 560 | 0 672 | 0 448 | 0 128 | * 2
x o3o3o *c3o3o3o3x . . . . . . . . | 28 | 1 12 | 12 60 | 60 160 | 160 240 | 240 192 | 192 32 32 | 32 32 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x . . . . . . . | 2 | 14 * ♦ 12 0 | 60 0 | 160 0 | 240 0 | 192 0 0 | 32 32 0 . . . . . . . x | 2 | * 168 | 1 10 | 10 40 | 40 80 | 80 80 | 80 16 16 | 16 16 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x . . . . . . x | 4 | 2 2 | 84 * ♦ 10 0 | 40 0 | 80 0 | 80 0 0 | 16 16 0 . . . . . . o3x | 3 | 0 3 | * 560 | 1 8 | 8 24 | 24 32 | 32 8 8 | 8 8 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x . . . . . o3x ♦ 6 | 3 6 | 3 2 | 280 * ♦ 8 0 | 24 0 | 32 0 0 | 8 8 0 . . . . . o3o3x ♦ 4 | 0 6 | 0 4 | * 1120 | 1 6 | 6 12 | 12 4 4 | 4 4 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x . . . . o3o3x ♦ 8 | 4 12 | 6 8 | 4 2 | 560 * ♦ 6 0 | 12 0 0 | 4 4 0 . . . . o3o3o3x ♦ 5 | 0 10 | 0 10 | 0 5 | * 1344 | 1 4 | 4 2 2 | 2 2 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x . . . o3o3o3x ♦ 10 | 5 20 | 10 20 | 10 10 | 5 2 | 672 * | 4 0 0 | 2 2 0 . . o . *c3o3o3o3x ♦ 6 | 0 15 | 0 20 | 0 15 | 0 6 | * 896 | 1 1 1 | 1 1 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x . o . *c3o3o3o3x ♦ 12 | 6 30 | 15 40 | 20 30 | 15 12 | 6 2 | 448 * * | 1 1 0 . o3o . *c3o3o3o3x ♦ 7 | 0 21 | 0 35 | 0 35 | 0 21 | 0 7 | * 128 * | 1 0 1 . . o3o *c3o3o3o3x ♦ 7 | 0 21 | 0 35 | 0 35 | 0 21 | 0 7 | * * 128 | 0 1 1 -------------------+----+--------+--------+----------+----------+---------+-------------+-------- x o3o . *c3o3o3o3x ♦ 14 | 7 42 | 21 70 | 35 70 | 35 42 | 21 14 | 7 2 0 | 64 * * x . o3o *c3o3o3o3x ♦ 14 | 7 42 | 21 70 | 35 70 | 35 42 | 21 14 | 7 0 2 | * 64 * . o3o3o *c3o3o3o3x ♦ 14 | 0 84 | 0 280 | 0 560 | 0 672 | 0 448 | 0 64 64 | * * 2
xx3oo3oo3oo3oo3oo4oo&#x → height = 1
(zee || zee)
o.3o.3o.3o.3o.3o.4o. | 14 * | 12 1 0 | 60 12 0 | 160 60 0 | 240 160 0 | 192 240 0 | 64 192 0 | 1 64 0
.o3.o3.o3.o3.o3.o4.o | * 14 | 0 1 12 | 0 12 60 | 0 60 160 | 0 160 240 | 0 240 192 | 0 192 64 | 0 64 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x. .. .. .. .. .. .. | 2 0 | 84 * * | 10 1 0 | 40 10 0 | 80 40 0 | 80 80 0 | 32 80 0 | 1 32 0
oo3oo3oo3oo3oo3oo4oo&#x | 1 1 | * 14 * ♦ 0 12 0 | 0 60 0 | 0 160 0 | 0 240 0 | 0 192 0 | 0 64 0
.x .. .. .. .. .. .. | 0 2 | * * 84 | 0 1 10 | 0 10 40 | 0 40 80 | 0 80 80 | 0 80 32 | 0 32 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o. .. .. .. .. .. | 3 0 | 3 0 0 | 280 * * | 8 1 0 | 24 8 0 | 32 24 0 | 16 32 0 | 1 16 0
xx .. .. .. .. .. ..&#x | 2 2 | 1 2 1 | * 84 * ♦ 0 10 0 | 0 40 0 | 0 80 0 | 0 80 0 | 0 32 0
.x3.o .. .. .. .. .. | 0 3 | 0 0 3 | * * 280 | 0 1 8 | 0 8 24 | 0 24 32 | 0 32 16 | 0 16 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o. .. .. .. .. ♦ 4 0 | 6 0 0 | 4 0 0 | 560 * * | 6 1 0 | 12 6 0 | 8 12 0 | 1 8 0
xx3oo .. .. .. .. ..&#x ♦ 3 3 | 3 3 3 | 1 3 1 | * 280 * ♦ 0 8 0 | 0 24 0 | 0 32 0 | 0 16 0
.x3.o3.o .. .. .. .. ♦ 0 4 | 0 0 6 | 0 0 4 | * * 560 | 0 1 6 | 0 6 12 | 0 12 8 | 0 8 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o. .. .. .. ♦ 5 0 | 10 0 0 | 10 0 0 | 5 0 0 | 672 * * | 4 1 0 | 4 4 0 | 1 4 0
xx3oo3oo .. .. .. ..&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 1 4 1 | * 560 * ♦ 0 6 0 | 0 12 0 | 0 8 0
.x3.o3.o3.o .. .. .. ♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 5 | * * 672 | 0 1 4 | 0 4 4 | 0 4 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o.3o. .. .. ♦ 6 0 | 15 0 0 | 20 0 0 | 15 0 0 | 6 0 0 | 448 * * | 2 1 0 | 1 2 0
xx3oo3oo3oo .. .. ..&#x ♦ 5 5 | 10 5 10 | 10 10 10 | 5 10 5 | 1 5 1 | * 672 * | 0 4 0 | 0 4 0
.x3.o3.o3.o3.o .. .. ♦ 0 6 | 0 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 448 | 0 1 2 | 0 2 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o.3o.3o. .. ♦ 7 0 | 21 0 0 | 35 0 0 | 35 0 0 | 21 0 0 | 7 0 0 | 128 * * | 1 1 0
xx3oo3oo3oo3oo .. ..&#x ♦ 6 6 | 15 6 15 | 20 15 20 | 15 20 15 | 6 15 6 | 1 6 1 | * 448 * | 0 2 0
.x3.o3.o3.o3.o3.o .. ♦ 0 7 | 0 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * 128 | 0 1 1
------------------------+-------+----------+------------+-------------+-------------+-------------+-------------+--------
x.3o.3o.3o.3o.3o.4o. ♦ 14 0 | 84 0 0 | 280 0 0 | 560 0 0 | 672 0 0 | 448 0 0 | 128 0 0 | 1 * *
xx3oo3oo3oo3oo3oo ..&#x ♦ 7 7 | 21 7 21 | 35 21 35 | 35 35 35 | 21 35 21 | 7 21 7 | 1 7 1 | * 128 *
.x3.o3.o3.o3.o3.o4.o ♦ 0 14 | 0 0 84 | 0 0 280 | 0 0 560 | 0 0 672 | 0 0 448 | 0 0 128 | * * 1
oo3oo3oo *b3oo3oo3oo3xx&#x → height = 1
(zee || zee)
o.3o.3o. *b3o.3o.3o.3o. | 14 * | 12 1 0 | 60 12 0 | 160 60 0 | 240 160 0 | 192 240 0 | 32 32 192 0 0 | 1 32 32 0
.o3.o3.o *b3.o3.o3.o3.o | * 14 | 0 1 12 | 0 12 60 | 0 60 160 | 0 160 240 | 0 240 192 | 0 0 192 32 32 | 0 32 32 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. .. .. .. .. x. | 2 0 | 84 * * | 10 1 0 | 40 10 0 | 80 40 0 | 80 80 0 | 16 16 80 0 0 | 1 16 16 0
oo3oo3oo *b3oo3oo3oo3oo&#x | 1 1 | * 14 * ♦ 0 12 0 | 0 60 0 | 0 160 0 | 0 240 0 | 0 0 192 0 0 | 0 32 32 0
.. .. .. .. .. .. .x | 0 2 | * * 84 | 0 1 10 | 0 10 40 | 0 40 80 | 0 80 80 | 0 0 80 16 16 | 0 16 16 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. .. .. .. o.3x. | 3 0 | 3 0 0 | 280 * * | 8 1 0 | 24 8 0 | 32 24 0 | 8 8 32 0 0 | 1 8 8 0
.. .. .. .. .. .. xx&#x | 2 2 | 1 2 1 | * 84 * ♦ 0 10 0 | 0 40 0 | 0 80 0 | 0 0 80 0 0 | 0 16 16 0
.. .. .. .. .. .o3.x | 0 3 | 0 0 3 | * * 280 | 0 1 8 | 0 8 24 | 0 24 32 | 0 0 32 8 8 | 0 8 8 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. .. .. o.3o.3x. ♦ 4 0 | 6 0 0 | 4 0 0 | 560 * * | 6 1 0 | 12 6 0 | 4 4 12 0 0 | 1 4 4 0
.. .. .. .. .. oo3xx&#x ♦ 3 3 | 3 3 3 | 1 3 1 | * 280 * ♦ 0 8 0 | 0 24 0 | 0 0 32 0 0 | 0 8 8 0
.. .. .. .. .o3.o3.x ♦ 0 4 | 0 0 6 | 0 0 4 | * * 560 | 0 1 6 | 0 6 12 | 0 0 12 4 4 | 0 4 4 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. .. .. o.3o.3o.3x. ♦ 5 0 | 10 0 0 | 10 0 0 | 5 0 0 | 672 * * | 4 1 0 | 2 2 4 0 0 | 1 2 2 0
.. .. .. .. oo3oo3xx&#x ♦ 4 4 | 6 4 6 | 4 6 4 | 1 4 1 | * 560 * ♦ 0 6 0 | 0 0 12 0 0 | 0 4 4 0
.. .. .. .o3.o3.o3.x ♦ 0 5 | 0 0 10 | 0 0 10 | 0 0 5 | * * 672 | 0 1 4 | 0 0 4 2 2 | 0 2 2 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
.. o. .. *b3o.3o.3o.3x. ♦ 6 0 | 15 0 0 | 20 0 0 | 15 0 0 | 6 0 0 | 448 * * | 1 1 1 0 0 | 1 1 1 0
.. .. .. oo3oo3oo3xx&#x ♦ 5 5 | 10 5 10 | 10 10 10 | 5 10 5 | 1 5 1 | * 672 * | 0 0 4 0 0 | 0 2 2 0
.. .o .. *b3.o3.o3.o3.x ♦ 0 6 | 0 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 448 | 0 0 1 1 1 | 0 1 1 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
o.3o. .. *b3o.3o.3o.3x. ♦ 7 0 | 21 0 0 | 35 0 0 | 35 0 0 | 21 0 0 | 7 0 0 | 64 * * * * | 1 1 0 0
.. o.3o. *b3o.3o.3o.3x. ♦ 7 0 | 21 0 0 | 35 0 0 | 35 0 0 | 21 0 0 | 7 0 0 | * 64 * * * | 1 0 1 0
.. oo .. *b3oo3oo3oo3xx&#x ♦ 6 6 | 15 6 15 | 20 15 20 | 15 20 15 | 6 15 6 | 1 6 1 | * * 448 * * | 0 1 1 0
.o3.o .. *b3.o3.o3.o3.x ♦ 0 7 | 0 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * * 64 * | 0 1 0 1
.. .o3.o *b3.o3.o3.o3.x ♦ 0 7 | 0 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * * * 64 | 0 0 1 1
---------------------------+-------+----------+------------+-------------+-------------+-------------+-----------------+----------
o.3o.3o. *b3o.3o.3o.3x. ♦ 14 0 | 84 0 0 | 280 0 0 | 560 0 0 | 672 0 0 | 448 0 0 | 64 64 0 0 0 | 1 * * *
oo3oo .. *b3oo3oo3oo3xx&#x ♦ 7 7 | 21 7 21 | 35 21 35 | 35 35 35 | 21 35 21 | 7 21 7 | 1 0 7 1 0 | * 64 * *
.. oo3oo *b3oo3oo3oo3xx&#x ♦ 7 7 | 21 7 21 | 35 21 35 | 35 35 35 | 21 35 21 | 7 21 7 | 0 1 7 0 1 | * * 64 *
.o3.o3.o *b3.o3.o3.o3.x ♦ 0 14 | 0 0 84 | 0 0 280 | 0 0 560 | 0 0 672 | 0 0 448 | 0 0 0 64 64 | * * * 1
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