vertex figure of broc
- more general:
- n,pen-dip
- general polytopal classes:
- Wythoffian polypeta segmentopeta lace simplices
links
| Acronym | trapen |
| Name |
triangle - pentachoron duoprism, vertex figure of broc |
| Circumradius | sqrt(11/15) = 0.856349 |
| Volume | sqrt(15)/384 = 0.010086 |
| Face vector | 15, 45, 65, 55, 28, 8 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o x3o3o3o . . . . . . | 15 | 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2 ------------+----+-------+---------+----------+---------+---- x . . . . . | 2 | 15 * | 1 4 0 | 4 6 0 | 6 4 0 | 4 1 . . x . . . | 2 | * 30 | 0 2 3 | 1 6 3 | 3 6 1 | 3 2 ------------+----+-------+---------+----------+---------+---- x3o . . . . | 3 | 3 0 | 5 * * ♦ 4 0 0 | 6 0 0 | 4 0 x . x . . . | 4 | 2 2 | * 30 * | 1 3 0 | 3 3 0 | 3 1 . . x3o . . | 3 | 0 3 | * * 30 | 0 2 2 | 1 4 1 | 2 2 ------------+----+-------+---------+----------+---------+---- x3o x . . . ♦ 6 | 6 3 | 2 3 0 | 10 * * | 3 0 0 | 3 0 x . x3o . . ♦ 6 | 3 6 | 0 3 2 | * 30 * | 1 2 0 | 2 1 . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * 15 | 0 2 1 | 1 2 ------------+----+-------+---------+----------+---------+---- x3o x3o . . ♦ 9 | 9 9 | 3 9 3 | 3 3 0 | 10 * * | 2 0 x . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 4 2 | * 15 * | 1 1 . . x3o3o3o ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 3 | 0 2 ------------+----+-------+---------+----------+---------+---- x3o x3o3o . ♦ 12 | 12 18 | 4 18 12 | 6 12 3 | 4 3 0 | 5 * x . x3o3o3o ♦ 10 | 5 20 | 0 10 20 | 0 10 10 | 0 5 2 | * 3
ox xx3oo3oo3oo&#x → height = sqrt(3)/2 = 0.866025
(pen || penp)
o. o.3o.3o.3o. | 5 * | 4 2 0 0 | 6 1 8 0 0 | 4 4 12 0 0 | 1 6 8 0 0 | 4 2 0
.o .o3.o3.o3.o | * 10 | 0 1 1 4 | 0 1 4 4 6 | 0 4 6 6 4 | 0 6 4 4 1 | 4 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x. .. .. .. | 2 0 | 10 * * * | 3 0 2 0 0 | 3 1 6 0 0 | 1 3 6 0 0 | 3 2 0
oo oo3oo3oo3oo&#x | 1 1 | * 10 * * | 0 1 4 0 0 | 0 4 6 0 0 | 0 6 4 0 0 | 4 1 0
.x .. .. .. .. | 0 2 | * * 5 * | 0 1 0 4 0 | 0 4 0 6 0 | 0 6 0 4 0 | 4 0 1
.. .x .. .. .. | 0 2 | * * * 20 | 0 0 1 1 3 | 0 1 3 3 3 | 0 3 3 3 1 | 3 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x.3o. .. .. | 3 0 | 3 0 0 0 | 10 * * * * | 2 0 2 0 0 | 1 1 4 0 0 | 2 2 0
ox .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 5 * * * ♦ 0 4 0 0 0 | 0 6 0 0 0 | 4 0 0
.. xx .. .. ..&#x | 2 2 | 1 2 0 1 | * * 20 * * | 0 1 3 0 0 | 0 3 3 0 0 | 3 1 0
.x .x .. .. .. | 0 4 | 0 0 2 2 | * * * 10 * | 0 1 0 3 0 | 0 3 0 3 0 | 3 0 1
.. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * * 20 | 0 0 1 1 2 | 0 1 2 2 1 | 2 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x.3o.3o. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 5 * * * * | 1 0 2 0 0 | 1 2 0
ox xx .. .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | * 10 * * * | 0 3 0 0 0 | 3 0 0
.. xx3oo .. ..&#x ♦ 3 3 | 3 3 0 3 | 1 0 3 0 1 | * * 20 * * | 0 1 2 0 0 | 2 1 0
.x .x3.o .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 3 2 | * * * 10 * | 0 1 0 2 0 | 2 0 1
.. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * 10 | 0 0 1 1 1 | 1 1 1
------------------+------+------------+---------------+---------------+-------------+------
.. x.3o.3o.3o. ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 | 5 0 0 0 0 | 1 * * * * | 0 2 0
ox xx3oo .. ..&#x ♦ 3 6 | 3 6 3 6 | 1 3 6 3 2 | 0 3 2 1 0 | * 10 * * * | 2 0 0
.. xx3oo3oo ..&#x ♦ 4 4 | 6 4 0 6 | 4 0 6 0 4 | 1 0 4 0 1 | * * 10 * * | 1 1 0
.x .x3.o3.o .. ♦ 0 8 | 0 0 4 12 | 0 0 0 6 8 | 0 0 0 4 2 | * * * 5 * | 1 0 1
.. .x3.o3.o3.o ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 5 | * * * * 2 | 0 1 1
------------------+------+------------+---------------+---------------+-------------+------
ox xx3oo3oo ..&#x ♦ 4 8 | 6 8 4 12 | 4 4 12 6 8 | 1 6 8 4 2 | 0 4 2 1 0 | 5 * *
.. xx3oo3oo3oo&#x ♦ 5 5 | 10 5 0 10 | 10 0 10 0 10 | 5 0 10 0 5 | 1 0 5 0 1 | * 2 *
.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 | * * 1
xx3oo ox3oo3oo&#x → height = sqrt(5/8) = 0.790569
({3} || tratet)
o.3o. o.3o.3o. | 3 * | 2 4 0 0 | 1 8 6 0 0 0 | 4 12 4 0 0 0 | 6 8 1 0 0 | 4 2 0
.o3.o .o3.o3.o | * 12 | 0 1 2 3 | 0 2 3 1 6 3 | 1 6 3 3 6 1 | 3 6 1 3 2 | 3 2 1
------------------+------+------------+-----------------+----------------+------------+------
x. .. .. .. .. | 2 0 | 3 * * * | 1 4 0 0 0 0 | 4 6 0 0 0 0 | 6 4 0 0 0 | 4 1 0
oo3oo oo3oo3oo&#x | 1 1 | * 12 * * | 0 2 3 0 0 0 | 1 6 3 0 0 0 | 3 6 1 0 0 | 3 2 0
.x .. .. .. .. | 0 2 | * * 12 * | 0 1 0 1 3 0 | 1 3 0 3 3 0 | 3 3 0 3 1 | 3 1 1
.. .. .x .. .. | 0 2 | * * * 18 | 0 0 1 0 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
------------------+------+------------+-----------------+----------------+------------+------
x.3o. .. .. .. | 3 0 | 3 0 0 0 | 1 * * * * * ♦ 4 0 0 0 0 0 | 6 0 0 0 0 | 4 0 0
xx .. .. .. ..&#x | 2 2 | 1 2 1 0 | * 12 * * * * | 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0
.. .. ox .. ..&#x | 1 2 | 0 2 0 1 | * * 18 * * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x3.o .. .. .. | 0 3 | 0 0 3 0 | * * * 4 * * | 1 0 0 3 0 0 | 3 0 0 3 0 | 3 0 1
.x .. .x .. .. | 0 4 | 0 0 2 2 | * * * * 18 * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x3.o .. | 0 3 | 0 0 0 3 | * * * * * 12 | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
------------------+------+------------+-----------------+----------------+------------+------
xx3oo .. .. ..&#x ♦ 3 3 | 3 3 3 0 | 1 3 0 1 0 0 | 4 * * * * * | 3 0 0 0 0 | 3 0 0
xx .. ox .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 1 0 | * 18 * * * * | 1 2 0 0 0 | 2 1 0
.. .. ox3oo ..&#x ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * 12 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .x .. .. ♦ 0 6 | 0 0 6 3 | 0 0 0 2 3 0 | * * * 6 * * | 1 0 0 2 0 | 2 0 1
.x .. .x3.o .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 2 | * * * * 12 * | 0 1 0 1 1 | 1 1 1
.. .. .x3.o3.o ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 4 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
------------------+------+------------+-----------------+----------------+------------+------
xx3oo ox .. ..&#x ♦ 3 6 | 3 6 6 3 | 1 6 3 2 3 0 | 2 3 0 1 0 0 | 6 * * * * | 2 0 0
xx .. ox3oo ..&#x ♦ 2 6 | 1 6 3 6 | 0 3 6 0 3 2 | 0 3 2 0 1 0 | * 12 * * * | 1 1 0
.. .. ox3oo3oo&#x ♦ 1 4 | 0 4 0 6 | 0 0 6 0 0 4 | 0 0 4 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x3.o .. ♦ 0 9 | 0 0 9 9 | 0 0 0 3 9 3 | 0 0 0 3 3 0 | * * * 4 * | 1 0 1
.x .. .x3.o3.o. ♦ 0 8 | 0 0 4 12 | 0 0 0 0 6 8 | 0 0 0 0 4 2 | * * * * 3 | 0 1 1
------------------+------+------------+-----------------+----------------+------------+------
xx3oo ox3oo ..&#x ♦ 3 9 | 3 9 9 9 | 1 9 9 3 9 3 | 3 9 3 3 3 0 | 3 3 0 1 0 | 4 * *
xx .. ox3oo3oo&#x ♦ 2 8 | 1 8 4 12 | 0 4 12 0 6 8 | 0 6 8 0 4 2 | 0 4 2 0 1 | * 3 *
.x3.o .x3.o3.o. ♦ 0 12 | 0 0 12 18 | 0 0 0 4 18 12 | 0 0 0 6 12 3 | 0 0 0 4 3 | * * 1
xxx3ooo3ooo3ooo&#x → all pairwise heights = 1 o..3o..3o..3o.. & | 15 | 4 2 | 6 8 1 | 4 12 4 | 1 8 6 | 2 4 ---------------------+----+-------+---------+----------+---------+---- x.. ... ... ... & | 2 | 30 * | 3 2 0 | 3 6 1 | 1 6 3 | 2 3 oo.3oo.3oo.3oo.&#x & | 2 | * 15 | 0 4 1 | 0 6 4 | 0 4 6 | 1 4 ---------------------+----+-------+---------+----------+---------+---- x..3o.. ... ... & | 3 | 3 0 | 30 * * | 2 2 0 | 1 4 1 | 2 2 xx. ... ... ...&#x & | 4 | 2 2 | * 30 * | 0 3 1 | 0 3 3 | 1 3 ooo3ooo3ooo3ooo&#x | 3 | 0 3 | * * 5 ♦ 0 0 4 | 0 0 6 | 0 4 ---------------------+----+-------+---------+----------+---------+---- x..3o..3o.. ... & ♦ 4 | 6 0 | 4 0 0 | 15 * * | 1 2 0 | 2 1 xx.3oo. ... ...&#x & ♦ 6 | 6 3 | 2 3 0 | * 30 * | 0 2 1 | 1 2 xxx ... ... ...&#x ♦ 6 | 3 6 | 0 3 2 | * * 10 | 0 0 3 | 0 3 ---------------------+----+-------+---------+----------+---------+---- x..3o..3o..3o.. & ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 3 * * | 2 0 xx.3oo.3oo. ...&#x & ♦ 8 | 12 4 | 8 6 0 | 2 4 0 | * 15 * | 1 1 xxx3ooo ... ...&#x ♦ 9 | 9 9 | 3 9 3 | 0 3 3 | * * 10 | 0 2 ---------------------+----+-------+---------+----------+---------+---- xx.3oo.3oo.3oo.&#x & ♦ 10 | 20 5 | 20 10 0 | 10 10 0 | 2 5 0 | 3 * xxx3ooo3ooo ...&#x ♦ 12 | 18 12 | 12 18 4 | 3 12 6 | 0 3 4 | * 5
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