vertex figure of breday
- general polytopal classes:
- Wythoffian polyzetta segmentozetta
links
| Acronym | trihop |
| Name |
triangle - heptapenton duoprism, vertex figure of breday |
| Circumradius | 4/sqrt(21) = 0.872872 |
| Volume | sqrt(21)/23040 = 0.00019890 |
| Face vector | 21, 84, 175, 231, 203, 119, 45, 10 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o x3o3o3o3o3o . . . . . . . . | 21 | 2 6 | 1 12 15 | 6 30 20 | 15 40 15 | 20 30 6 | 15 12 1 | 6 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x . . . . . . . | 2 | 21 * | 1 6 0 | 6 15 0 | 15 20 0 | 20 15 0 | 15 6 0 | 6 1 . . x . . . . . | 2 | * 63 | 0 2 5 | 1 10 10 | 5 20 10 | 10 20 5 | 10 10 1 | 5 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x3o . . . . . . | 3 | 3 0 | 7 * * ♦ 6 0 0 | 15 0 0 | 20 0 0 | 15 0 0 | 6 0 x . x . . . . . | 4 | 2 2 | * 63 * | 1 5 0 | 5 10 0 | 10 10 0 | 10 5 0 | 5 1 . . x3o . . . . | 3 | 0 3 | * * 105 | 0 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x3o x . . . . . ♦ 6 | 6 3 | 2 3 0 | 21 * * ♦ 5 0 0 | 10 0 0 | 10 0 0 | 5 0 x . x3o . . . . ♦ 6 | 3 6 | 0 3 2 | * 105 * | 1 4 0 | 4 6 0 | 6 4 0 | 4 1 . . x3o3o . . . ♦ 4 | 0 6 | 0 0 4 | * * 105 | 0 2 3 | 1 6 3 | 3 6 1 | 3 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x3o x3o . . . . ♦ 9 | 9 9 | 3 9 3 | 3 3 0 | 35 * * ♦ 4 0 0 | 6 0 0 | 4 0 x . x3o3o . . . ♦ 8 | 4 12 | 0 6 8 | 0 4 2 | * 105 * | 1 3 0 | 3 3 0 | 3 1 . . x3o3o3o . . ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 63 | 0 2 2 | 1 4 1 | 2 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x3o x3o3o . . . ♦ 12 | 12 18 | 4 18 12 | 6 12 3 | 4 3 0 | 35 * * | 3 0 0 | 3 0 x . x3o3o3o . . ♦ 10 | 5 20 | 0 10 20 | 0 10 10 | 0 5 2 | * 63 * | 1 2 0 | 2 1 . . x3o3o3o3o . ♦ 6 | 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 21 | 0 2 1 | 1 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x3o x3o3o3o . . ♦ 15 | 15 30 | 5 30 30 | 10 30 15 | 10 15 3 | 5 3 0 | 21 * * | 2 0 x . x3o3o3o3o . ♦ 12 | 6 30 | 0 15 40 | 0 20 30 | 0 15 12 | 0 6 2 | * 21 * | 1 1 . . x3o3o3o3o3o ♦ 7 | 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * 3 | 0 2 ----------------+----+-------+----------+------------+-----------+----------+---------+---- x3o x3o3o3o3o . ♦ 18 | 18 45 | 6 45 60 | 15 60 45 | 20 45 18 | 15 18 3 | 6 3 0 | 7 * x . x3o3o3o3o3o ♦ 14 | 7 42 | 0 21 70 | 0 35 70 | 0 35 42 | 0 21 14 | 0 7 2 | * 3
ox xx3oo3oo3oo3oo3oo&#x → height = sqrt(3)/2 = 0.866025
(hop || hopip)
o. o.3o.3o.3o.3o.3o. | 7 * | 6 2 0 0 | 15 1 12 0 0 | 20 6 30 0 0 | 15 15 40 0 0 | 6 20 30 0 0 | 1 15 12 0 0 | 6 2 0
.o .o3.o3.o3.o3.o3.o | * 14 | 0 1 1 6 | 0 1 6 6 15 | 0 6 15 15 20 | 0 15 20 20 15 | 0 20 15 15 6 | 0 15 6 6 1 | 6 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x. .. .. .. .. .. | 2 0 | 21 * * * | 5 0 2 0 0 | 10 1 10 0 0 | 10 5 20 0 0 | 5 10 20 0 0 | 1 10 10 0 0 | 5 2 0
oo oo3oo3oo3oo3oo3oo&#x | 1 1 | * 14 * * | 0 1 6 0 0 | 0 6 15 0 0 | 0 15 20 0 0 | 0 20 15 0 0 | 0 15 6 0 0 | 6 1 0
.x .. .. .. .. .. .. | 0 2 | * * 7 * | 0 1 0 6 0 | 0 6 0 15 0 | 0 15 0 20 0 | 0 20 0 15 0 | 0 15 0 6 0 | 6 0 1
.. .x .. .. .. .. .. | 0 2 | * * * 42 | 0 0 1 1 5 | 0 1 5 5 10 | 0 5 10 10 10 | 0 10 10 10 5 | 0 10 5 5 1 | 5 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o. .. .. .. .. | 3 0 | 3 0 0 0 | 35 * * * * | 4 0 2 0 0 | 6 1 8 0 0 | 4 4 12 0 0 | 1 6 8 0 0 | 4 2 0
ox .. .. .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 7 * * * ♦ 0 6 0 0 0 | 0 15 0 0 0 | 0 20 0 0 0 | 0 15 0 0 0 | 6 0 0
.. xx .. .. .. .. ..&#x | 2 2 | 1 2 0 1 | * * 42 * * | 0 1 5 0 0 | 0 5 10 0 0 | 0 10 10 0 0 | 0 10 5 0 0 | 5 1 0
.x .x .. .. .. .. .. | 0 4 | 0 0 2 2 | * * * 21 * | 0 1 0 5 0 | 0 5 0 10 0 | 0 10 0 10 0 | 0 10 0 5 0 | 5 0 1
.. .x3.o .. .. .. .. | 0 3 | 0 0 0 3 | * * * * 70 | 0 0 1 1 4 | 0 1 4 4 6 | 0 4 6 6 4 | 0 6 4 4 1 | 4 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 35 * * * * | 3 0 2 0 0 | 3 1 6 0 0 | 1 3 6 0 0 | 3 2 0
ox xx .. .. .. .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | * 21 * * * ♦ 0 5 0 0 0 | 0 10 0 0 0 | 0 10 0 0 0 | 5 0 0
.. xx3oo .. .. .. ..&#x ♦ 3 3 | 3 3 0 3 | 1 0 3 0 1 | * * 70 * * | 0 1 4 0 0 | 0 4 6 0 0 | 0 6 4 0 0 | 4 1 0
.x .x3.o .. .. .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 3 2 | * * * 35 * | 0 1 0 4 0 | 0 4 0 6 0 | 0 6 0 4 0 | 4 0 1
.. .x3.o3.o .. .. .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * 70 | 0 0 1 1 3 | 0 1 3 3 3 | 0 3 3 3 1 | 3 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o.3o.3o. .. .. ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 | 5 0 0 0 0 | 21 * * * * | 2 0 2 0 0 | 1 1 4 0 0 | 2 2 0
ox xx3oo .. .. .. ..&#x ♦ 3 6 | 3 6 3 6 | 1 3 6 3 2 | 0 3 2 1 0 | * 35 * * * ♦ 0 4 0 0 0 | 0 6 0 0 0 | 4 0 0
.. xx3oo3oo .. .. ..&#x ♦ 4 4 | 6 4 0 6 | 4 0 6 0 4 | 1 0 4 0 1 | * * 70 * * | 0 1 3 0 0 | 0 3 3 0 0 | 3 1 0
.x .x3.o3.o .. .. .. ♦ 0 8 | 0 0 4 12 | 0 0 0 6 8 | 0 0 0 4 2 | * * * 35 * | 0 1 0 3 0 | 0 3 0 3 0 | 3 0 1
.. .x3.o3.o3.o .. .. ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 5 | * * * * 42 | 0 0 1 1 2 | 0 1 2 2 1 | 2 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o.3o.3o.3o. .. ♦ 6 0 | 15 0 0 0 | 20 0 0 0 0 | 15 0 0 0 0 | 6 0 0 0 0 | 7 * * * * | 1 0 2 0 0 | 1 2 0
ox xx3oo3oo .. .. ..&#x ♦ 4 8 | 6 8 4 12 | 4 4 12 6 8 | 1 6 8 4 2 | 0 4 2 1 0 | * 35 * * * | 0 3 0 0 0 | 3 0 0
.. xx3oo3oo3oo .. ..&#x ♦ 5 5 | 10 5 0 10 | 10 0 10 0 10 | 5 0 10 0 5 | 1 0 5 0 1 | * * 42 * * | 0 1 2 0 0 | 2 1 0
.x .x3.o3.o3.o .. .. ♦ 0 10 | 0 0 5 20 | 0 0 0 10 20 | 0 0 0 10 10 | 0 0 0 5 2 | * * * 21 * | 0 1 0 2 0 | 2 0 1
.. .x3.o3.o3.o3.o .. ♦ 0 6 | 0 0 0 15 | 0 0 0 0 20 | 0 0 0 0 15 | 0 0 0 0 6 | * * * * 14 | 0 0 1 1 1 | 1 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. .x3.o3.o3.o3.o3.o ♦ 7 0 | 21 0 0 0 | 35 0 0 0 0 | 35 0 0 0 0 | 21 0 0 0 0 | 7 0 0 0 0 | 1 * * * * | 0 2 0
ox xx3oo3oo3oo .. ..&#x ♦ 5 10 | 10 10 5 20 | 10 5 20 10 20 | 5 10 20 10 10 | 1 10 10 5 2 | 0 5 2 1 0 | * 21 * * * | 2 0 0
.. xx3oo3oo3oo3oo ..&#x ♦ 6 6 | 15 6 0 15 | 20 0 15 0 20 | 15 0 20 0 15 | 6 0 15 0 6 | 1 0 6 0 1 | * * 14 * * | 1 1 0
.x .x3.o3.o3.o3.o .. ♦ 0 12 | 0 0 6 30 | 0 0 0 15 40 | 0 0 0 20 30 | 0 0 0 15 12 | 0 0 0 6 2 | * * * 7 * | 1 0 1
.. .x3.o3.o3.o3.o3.o ♦ 0 7 | 0 0 0 21 | 0 0 0 0 35 | 0 0 0 0 35 | 0 0 0 0 21 | 0 0 0 0 7 | * * * * 2 | 0 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
ox xx3oo3oo3oo3oo ..&#x ♦ 6 12 | 15 12 6 30 | 20 6 30 15 40 | 15 15 40 20 30 | 6 20 30 15 12 | 1 15 12 6 2 | 0 6 2 1 0 | 7 * *
.. xx3oo3oo3oo3oo3oo&#x ♦ 7 7 | 21 7 0 21 | 35 0 21 0 35 | 35 0 35 0 35 | 21 0 35 0 21 | 7 0 21 0 7 | 1 0 7 0 1 | * 2 *
.x .x3.o3.o3.o3.o3.o ♦ 0 14 | 0 0 7 42 | 0 0 0 21 70 | 0 0 0 35 70 | 0 0 0 35 42 | 0 0 0 21 14 | 0 0 0 7 2 | * * 1
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