vertex figure of branq
- more general:
- n,rap-dip
- general polytopal classes:
- Wythoffian polypeta segmentopeta lace simplices
links
| Acronym | trarap |
| Name |
triangle - rectified-pentachoron duoprism, vertex figure of branq |
| Circumradius | sqrt(14/15) = 0.966092 |
| Volume | 11 sqrt(15)/384 = 0.110945 |
| Face vector | 30, 120, 190, 150, 63, 13 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o o3x3o3o . . . . . . | 30 | 2 6 | 1 12 3 6 | 6 6 12 3 2 | 3 6 6 4 1 | 3 2 2 ------------+----+-------+-------------+----------------+---------------+------ x . . . . . | 2 | 30 * | 1 6 0 0 | 6 3 6 0 0 | 3 6 3 2 0 | 3 2 1 . . . x . . | 2 | * 90 | 0 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ------------+----+-------+-------------+----------------+---------------+------ x3o . . . . | 3 | 3 0 | 10 * * * ♦ 6 0 0 0 0 | 3 6 0 0 0 | 3 2 0 x . . x . . | 4 | 2 2 | * 90 * * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 . . o3x . . | 3 | 0 3 | * * 30 * | 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 . . . x3o . | 3 | 0 3 | * * * 60 | 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ------------+----+-------+-------------+----------------+---------------+------ x3o . x . . ♦ 6 | 6 3 | 2 3 0 0 | 30 * * * * | 1 2 0 0 0 | 2 1 0 x . o3x . . ♦ 6 | 3 6 | 0 3 2 0 | * 30 * * * | 1 0 2 0 0 | 2 0 1 x . . x3o . ♦ 6 | 3 6 | 0 3 0 2 | * * 60 * * | 0 1 1 1 0 | 1 1 1 . . o3x3o . ♦ 6 | 0 12 | 0 0 4 4 | * * * 15 * | 0 0 2 0 1 | 1 0 2 . . . x3o3o ♦ 4 | 0 6 | 0 0 0 4 | * * * * 15 | 0 0 0 2 1 | 0 1 2 ------------+----+-------+-------------+----------------+---------------+------ x3o o3x . . ♦ 9 | 9 9 | 3 9 3 0 | 3 3 0 0 0 | 10 * * * * | 2 0 0 x3o . x3o . ♦ 9 | 9 9 | 3 9 0 3 | 3 0 3 0 0 | * 20 * * * | 1 1 0 x . o3x3o . ♦ 12 | 6 24 | 0 12 8 8 | 0 4 4 2 0 | * * 15 * * | 1 0 1 x . . x3o3o ♦ 8 | 4 12 | 0 6 0 8 | 0 0 4 0 2 | * * * 15 * | 0 1 1 . . o3x3o3o ♦ 10 | 0 30 | 0 0 10 20 | 0 0 0 5 5 | * * * * 3 | 0 0 2 ------------+----+-------+-------------+----------------+---------------+------ x3o o3x3o . ♦ 18 | 18 36 | 6 36 12 12 | 12 12 12 3 0 | 4 4 3 0 0 | 5 * * x3o . x3o3o ♦ 12 | 12 18 | 4 18 0 12 | 6 0 12 0 3 | 0 4 0 3 0 | * 5 * x . o3x3o3o ♦ 20 | 10 60 | 0 30 20 40 | 0 10 20 10 10 | 0 0 5 5 2 | * * 3
ox oo3xx3oo3oo&#x → height = sqrt(3)/2 = 0.866025
(rap || rappip)
o. o.3o.3o.3o. | 10 * | 6 2 0 0 | 3 6 1 12 0 0 0 | 3 2 6 6 12 0 0 0 0 | 1 3 6 6 4 0 0 0 | 3 2 2 0
.o .o3.o3.o3.o | * 20 | 0 1 1 6 | 0 0 1 6 6 3 6 | 0 0 6 3 6 3 6 3 2 | 0 3 6 3 2 3 2 1 | 3 2 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. .. x. .. .. | 2 0 | 30 * * * | 1 2 0 2 0 0 0 | 2 1 1 2 4 0 0 0 0 | 1 1 2 4 2 0 0 0 | 2 1 2 0
oo oo3oo3oo3oo&#x | 1 1 | * 20 * * | 0 0 1 6 0 0 0 | 0 0 6 3 6 0 0 0 0 | 0 3 6 3 2 0 0 0 | 3 2 1 0
.x .. .. .. .. | 0 2 | * * 10 * | 0 0 1 0 6 0 0 | 0 0 6 0 0 3 6 0 0 | 0 3 6 0 0 3 2 0 | 3 2 0 1
.. .. .x .. .. | 0 2 | * * * 60 | 0 0 0 1 1 1 2 | 0 0 1 1 2 1 2 2 1 | 0 1 2 2 1 2 1 1 | 2 1 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. o.3x. .. .. | 3 0 | 3 0 0 0 | 10 * * * * * * | 2 0 0 2 0 0 0 0 0 | 1 1 0 4 0 0 0 0 | 2 0 2 0
.. .. x.3o. .. | 3 0 | 3 0 0 0 | * 20 * * * * * | 1 1 0 0 2 0 0 0 0 | 1 0 1 2 2 0 0 0 | 1 1 2 0
ox .. .. .. ..&#x | 1 2 | 0 2 1 0 | * * 10 * * * * ♦ 0 0 6 0 0 0 0 0 0 | 0 3 6 0 0 0 0 0 | 3 2 0 0
.. .. xx .. ..&#x | 2 2 | 1 2 0 1 | * * * 60 * * * | 0 0 1 1 2 0 0 0 0 | 0 1 2 2 1 0 0 0 | 2 1 1 0
.x .. .x .. .. | 0 4 | 0 0 2 2 | * * * * 30 * * | 0 0 1 0 0 1 2 0 0 | 0 1 2 0 0 2 1 0 | 2 1 0 1
.. .o3.x .. .. | 0 3 | 0 0 0 3 | * * * * * 20 * | 0 0 0 1 0 1 0 2 0 | 0 1 0 2 0 2 0 1 | 2 0 1 1
.. .. .x3.o .. | 0 3 | 0 0 0 3 | * * * * * * 40 | 0 0 0 0 1 0 1 1 1 | 0 0 1 1 1 1 1 1 | 1 1 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. o.3x.3o. .. ♦ 6 0 | 12 0 0 0 | 4 4 0 0 0 0 0 | 5 * * * * * * * * | 1 0 0 2 0 0 0 0 | 1 0 2 0
.. .. x.3o.3o. ♦ 4 0 | 6 0 0 0 | 0 4 0 0 0 0 0 | * 5 * * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0
ox .. xx .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 0 2 2 1 0 0 | * * 30 * * * * * * | 0 1 2 0 0 0 0 0 | 2 1 0 0
.. oo3xx .. ..&#x ♦ 3 3 | 3 3 0 3 | 1 0 0 3 0 1 0 | * * * 20 * * * * * | 0 1 0 2 0 0 0 0 | 2 0 1 0
.. .. xx3oo ..&#x ♦ 3 3 | 3 3 0 3 | 0 1 0 3 0 0 1 | * * * * 40 * * * * | 0 0 1 1 1 0 0 0 | 1 1 1 0
.x .o3.x .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 2 0 | * * * * * 10 * * * | 0 1 0 0 0 2 0 0 | 2 0 0 1
.x .. .x3.o .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 0 2 | * * * * * * 20 * * | 0 0 1 0 0 1 1 0 | 1 1 0 1
.. .o3.x3.o .. ♦ 0 6 | 0 0 0 12 | 0 0 0 0 0 4 4 | * * * * * * * 10 * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.o3.o ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * * 10 | 0 0 0 0 1 0 1 1 | 0 1 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
.. o.3x.3o.3o. ♦ 10 0 | 30 0 0 0 | 10 20 0 0 0 0 0 | 5 5 0 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
ox oo3xx .. ..&#x ♦ 3 6 | 3 6 3 6 | 1 0 3 6 3 2 0 | 0 0 3 2 0 1 0 0 0 | * 10 * * * * * * | 2 0 0 0
ox .. xx3oo ..&#x ♦ 3 6 | 3 6 3 6 | 0 1 3 6 3 0 2 | 0 0 3 0 2 0 1 0 0 | * * 20 * * * * * | 1 1 0 0
.. oo3xx3oo ..&#x ♦ 6 6 | 12 6 0 12 | 4 4 0 12 0 4 4 | 1 0 0 4 4 0 0 1 0 | * * * 10 * * * * | 1 0 1 0
.. .. xx3oo3oo&#x ♦ 4 4 | 6 4 0 6 | 0 4 0 6 0 0 4 | 0 1 0 0 4 0 0 0 1 | * * * * 10 * * * | 0 1 1 0
.x .o3.x3.o .. ♦ 0 12 | 0 0 6 24 | 0 0 0 0 12 8 8 | 0 0 0 0 0 4 4 2 0 | * * * * * 5 * * | 1 0 0 1
.x .. .x3.o3.o ♦ 0 8 | 0 0 4 12 | 0 0 0 0 6 0 8 | 0 0 0 0 0 0 4 0 2 | * * * * * * 5 * | 0 1 0 1
.. .o3.x3.o3.o ♦ 0 10 | 0 0 0 30 | 0 0 0 0 0 10 20 | 0 0 0 0 0 0 0 5 5 | * * * * * * * 2 | 0 0 1 1
------------------+-------+-------------+----------------------+--------------------------+---------------------+--------
ox oo3xx3oo ..&#x ♦ 6 12 | 12 12 6 24 | 4 4 6 24 12 8 8 | 1 0 12 8 8 4 4 2 0 | 0 4 4 2 0 1 0 0 | 5 * * *
ox .. xx3oo3oo&#x ♦ 4 8 | 6 8 4 12 | 0 4 4 12 6 0 8 | 0 1 6 0 8 0 4 0 2 | 0 0 4 0 2 0 1 0 | * 5 * *
.. oo3xx3oo3oo&#x ♦ 10 10 | 30 10 0 30 | 10 20 0 30 0 10 20 | 5 5 0 10 20 0 0 5 5 | 1 0 0 5 5 0 0 1 | * * 2 *
.x .o3.x3.o3.o ♦ 0 20 | 0 0 10 60 | 0 0 0 0 30 20 40 | 0 0 0 0 0 10 20 10 10 | 0 0 0 0 0 5 5 2 | * * * 1
xx3oo xo3ox3oo&#x → height = sqrt(5/8) = 0.790569
(tratet || troct)
o.3o. o.3o.3o. | 12 * | 2 3 3 0 0 | 1 6 3 6 3 3 0 0 0 0 | 3 6 1 3 6 6 3 1 0 0 0 0 | 3 2 3 3 6 2 1 0 0 0 | 1 3 1 2 0
.o3.o .o3.o3.o | * 18 | 0 0 2 2 4 | 0 0 0 4 1 4 1 8 2 2 | 0 0 0 2 2 8 2 2 4 4 4 1 | 0 0 1 4 4 4 1 2 2 2 | 0 2 2 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x. .. .. .. .. | 2 0 | 12 * * * * | 1 3 0 3 0 0 0 0 0 0 | 3 3 0 3 3 3 0 0 0 0 0 0 | 3 1 3 3 3 1 0 0 0 0 | 1 3 1 1 0
.. .. x. .. .. | 2 0 | * 18 * * * | 0 2 2 0 1 0 0 0 0 0 | 1 4 1 0 2 0 2 0 0 0 0 0 | 2 2 1 0 4 0 1 0 0 0 | 1 2 0 2 0
oo3oo oo3oo3oo&#x | 1 1 | * * 36 * * | 0 0 0 2 1 2 0 0 0 0 | 0 0 0 1 2 4 2 1 0 0 0 0 | 0 0 1 2 4 2 1 0 0 0 | 0 2 1 2 0
.x .. .. .. .. | 0 2 | * * * 18 * | 0 0 0 2 0 0 1 4 0 0 | 0 0 0 2 1 4 0 0 4 2 2 0 | 0 0 1 4 2 2 0 2 2 1 | 0 2 2 1 1
.. .. .. .x .. | 0 2 | * * * * 36 | 0 0 0 0 0 1 0 2 1 1 | 0 0 0 0 0 2 1 1 1 2 2 1 | 0 0 0 1 2 2 1 1 1 2 | 0 1 1 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. .. .. .. | 3 0 | 3 0 0 0 0 | 4 * * * * * * * * * ♦ 3 0 0 3 0 0 0 0 0 0 0 0 | 3 0 3 3 0 0 0 0 0 0 | 1 3 1 0 0
x. .. x. .. .. | 4 0 | 2 2 0 0 0 | * 18 * * * * * * * * | 1 2 0 0 1 0 0 0 0 0 0 0 | 2 1 1 0 2 0 0 0 0 0 | 1 2 0 1 0
.. .. x.3o. .. | 3 0 | 0 3 0 0 0 | * * 12 * * * * * * * | 0 2 1 0 0 0 1 0 0 0 0 0 | 1 2 0 0 2 0 1 0 0 0 | 1 1 0 2 0
xx .. .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 36 * * * * * * | 0 0 0 1 1 2 0 0 0 0 0 0 | 0 0 1 2 2 1 0 0 0 0 | 0 2 1 1 0
.. .. xo .. ..&#x | 2 1 | 0 1 2 0 0 | * * * * 18 * * * * * | 0 0 0 0 2 0 2 0 0 0 0 0 | 0 0 1 0 4 0 1 0 0 0 | 0 2 0 2 0
.. .. .. ox ..&#x | 1 2 | 0 0 2 0 1 | * * * * * 36 * * * * | 0 0 0 0 0 2 1 1 0 0 0 0 | 0 0 0 1 2 2 1 0 0 0 | 0 1 1 2 0
.x3.o .. .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 6 * * * ♦ 0 0 0 2 0 0 0 0 4 0 0 0 | 0 0 1 4 0 0 0 2 2 0 | 0 2 2 0 1
.x .. .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * * * 36 * * | 0 0 0 0 0 1 0 0 1 1 1 0 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1
.. .. .o3.x .. | 0 3 | 0 0 0 0 3 | * * * * * * * * 12 * | 0 0 0 0 0 0 1 0 0 2 0 1 | 0 0 0 0 2 0 1 1 0 2 | 0 1 0 2 1
.. .. .. .x3.o | 0 3 | 0 0 0 0 3 | * * * * * * * * * 12 | 0 0 0 0 0 0 0 1 0 0 2 1 | 0 0 0 0 0 2 1 0 1 2 | 0 0 1 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. x. .. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * * * | 2 0 1 0 0 0 0 0 0 0 | 1 2 0 0 0
x. .. x.3o. .. ♦ 6 0 | 3 6 0 0 0 | 0 3 2 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 | 1 1 0 1 0
.. .. x.3o.3o. ♦ 4 0 | 0 6 0 0 0 | 0 0 4 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * | 0 2 0 0 0 0 1 0 0 0 | 1 0 0 2 0
xx3oo .. .. ..&#x ♦ 3 3 | 3 0 3 3 0 | 1 0 0 3 0 0 1 0 0 0 | * * * 12 * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 | 0 2 1 0 0
xx .. xo .. ..&#x ♦ 4 2 | 2 2 4 1 0 | 0 1 0 2 2 0 0 0 0 0 | * * * * 18 * * * * * * * | 0 0 1 0 2 0 0 0 0 0 | 0 2 0 1 0
xx .. .. ox ..&#x ♦ 2 4 | 1 0 4 2 2 | 0 0 0 2 0 2 0 1 0 0 | * * * * * 36 * * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0
.. .. xo3ox ..&#x ♦ 3 3 | 0 3 6 0 3 | 0 0 1 0 3 3 0 0 1 0 | * * * * * * 12 * * * * * | 0 0 0 0 2 0 1 0 0 0 | 0 1 0 2 0
.. .. .. ox3oo&#x ♦ 1 3 | 0 0 3 0 3 | 0 0 0 0 0 3 0 0 0 1 | * * * * * * * 12 * * * * | 0 0 0 0 0 2 1 0 0 0 | 0 0 1 2 0
.x3.o .. .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 0 | * * * * * * * * 12 * * * | 0 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1
.x .. .o3.x .. ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 3 2 0 | * * * * * * * * * 12 * * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.x .. .. .x3.o ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 3 0 2 | * * * * * * * * * * 12 * | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
.. .. .o3.x3.o ♦ 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * 3 | 0 0 0 0 0 0 1 0 0 2 | 0 0 0 2 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. x.3o. .. ♦ 9 0 | 9 9 0 0 0 | 3 9 3 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0
x. .. x.3o.3o. ♦ 8 0 | 4 12 0 0 0 | 0 6 8 0 0 0 0 0 0 0 | 0 4 2 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * | 1 0 0 1 0
xx3oo xo .. ..&#x ♦ 6 3 | 6 3 6 3 0 | 2 3 0 6 3 0 1 0 0 0 | 1 0 0 2 3 0 0 0 0 0 0 0 | * * 6 * * * * * * * | 0 2 0 0 0
xx3oo .. ox ..&#x ♦ 3 6 | 3 0 6 6 3 | 1 0 0 6 0 3 2 3 0 0 | 0 0 0 2 0 3 0 0 1 0 0 0 | * * * 12 * * * * * * | 0 1 1 0 0
xx .. xo3ox ..&#x ♦ 6 6 | 3 6 12 3 6 | 0 3 2 6 6 6 0 3 2 0 | 0 1 0 0 3 3 2 0 0 1 0 0 | * * * * 12 * * * * * | 0 1 0 1 0
xx .. .. ox3oo&#x ♦ 2 6 | 1 0 6 3 6 | 0 0 0 3 0 6 0 3 0 2 | 0 0 0 0 0 3 0 2 0 0 1 0 | * * * * * 12 * * * * | 0 0 1 1 0
.. .. xo3ox3oo&#x ♦ 4 6 | 0 6 12 0 12 | 0 0 4 0 6 12 0 0 4 4 | 0 0 1 0 0 0 4 4 0 0 0 1 | * * * * * * 3 * * * | 0 0 0 2 0
.x3.o .o3.x .. ♦ 0 9 | 0 0 0 9 9 | 0 0 0 0 0 0 3 9 3 0 | 0 0 0 0 0 0 0 0 3 3 0 0 | * * * * * * * 4 * * | 0 1 0 0 1
.x3.o .. .x3.o ♦ 0 9 | 0 0 0 9 9 | 0 0 0 0 0 0 3 9 0 3 | 0 0 0 0 0 0 0 0 3 0 3 0 | * * * * * * * * 4 * | 0 0 1 0 1
.x .. .o3.x3.o ♦ 0 12 | 0 0 0 6 24 | 0 0 0 0 0 0 0 12 8 8 | 0 0 0 0 0 0 0 0 0 4 4 2 | * * * * * * * * * 3 | 0 0 0 1 1
------------------+-------+----------------+-----------------------------+----------------------------------+------------------------+----------
x.3o. x.3o.3o. ♦ 12 0 | 12 18 0 0 0 | 4 18 12 0 0 0 0 0 0 0 | 6 12 3 0 0 0 0 0 0 0 0 0 | 4 3 0 0 0 0 0 0 0 0 | 1 * * * *
xx3oo xo3ox ..&#x ♦ 9 9 | 9 9 18 9 9 | 3 9 3 18 9 9 3 9 3 0 | 3 3 0 6 9 9 3 0 3 3 0 0 | 1 0 3 3 3 0 0 1 0 0 | * 4 * * *
xx3oo .. ox3oo&#x ♦ 3 9 | 3 0 9 9 9 | 1 0 0 9 0 9 3 9 0 3 | 0 0 0 3 0 9 0 3 3 0 3 0 | 0 0 0 3 0 3 0 0 1 0 | * * 4 * *
xx .. xo3ox3oo&#x ♦ 8 12 | 4 12 24 6 24 | 0 6 8 12 12 24 0 12 8 8 | 0 4 2 0 6 12 8 8 0 4 4 2 | 0 1 0 0 4 4 2 0 0 1 | * * * 3 *
.x3.o .o3.x3.o ♦ 0 18 | 0 0 0 18 36 | 0 0 0 0 0 0 6 36 12 12 | 0 0 0 0 0 0 0 0 12 12 12 3 | 0 0 0 0 0 0 0 4 4 3 | * * * * 1
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