vertex figure of borfy
- general polytopal classes:
- Wythoffian polyexa segmentoexa
links
| Acronym | trahin |
| Name |
triangle - hemipenteract duoprism, vertex figure of borfy |
| Circumradius | sqrt(23/24) = 0.978945 |
| Volume | 13 sqrt(6)/480 = 0.066340 |
| Face vector | 48, 288, 736, 920, 598, 201, 29 |
| Confer |
|
|
External links |
|
Incidence matrix according to Dynkin symbol
x3o x3o3o *d3o3o . . . . . . . | 48 | 2 10 | 1 20 30 | 10 60 10 20 | 30 20 40 5 5 | 10 20 10 10 1 | 5 5 2 -----------------+----+--------+------------+----------------+-------------------+---------------+-------- x . . . . . . | 2 | 48 * | 1 10 0 | 10 30 0 0 | 30 10 20 0 0 | 10 20 5 5 0 | 5 5 1 . . x . . . . | 2 | * 240 | 0 2 6 | 1 12 3 6 | 6 6 12 3 2 | 3 6 6 4 1 | 3 2 2 -----------------+----+--------+------------+----------------+-------------------+---------------+-------- x3o . . . . . | 3 | 3 0 | 16 * * ♦ 10 0 0 0 | 30 0 0 0 0 | 10 20 0 0 0 | 5 5 0 x . x . . . . | 4 | 2 2 | * 240 * | 1 6 0 0 | 6 3 6 0 0 | 3 6 3 2 0 | 3 2 1 . . x3o . . . | 3 | 0 3 | * * 480 | 0 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 -----------------+----+--------+------------+----------------+-------------------+---------------+-------- x3o x . . . . ♦ 6 | 6 3 | 2 3 0 | 80 * * * ♦ 6 0 0 0 0 | 3 6 0 0 0 | 3 2 0 x . x3o . . . ♦ 6 | 3 6 | 0 3 2 | * 480 * * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 . . x3o3o . . ♦ 4 | 0 6 | 0 0 4 | * * 120 * | 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 . . x3o . *d3o . ♦ 4 | 0 6 | 0 0 4 | * * * 240 | 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 -----------------+----+--------+------------+----------------+-------------------+---------------+-------- x3o x3o . . . ♦ 9 | 9 9 | 3 9 3 | 3 3 0 0 | 160 * * * * | 1 2 0 0 0 | 2 1 0 x . x3o3o . . ♦ 8 | 4 12 | 0 6 8 | 0 4 2 0 | * 120 * * * | 1 0 2 0 0 | 2 0 1 x . x3o . *d3o . ♦ 8 | 4 12 | 0 6 8 | 0 4 0 2 | * * 240 * * | 0 1 1 1 0 | 1 1 1 . . x3o3o *d3o . ♦ 8 | 0 24 | 0 0 32 | 0 0 8 8 | * * * 30 * | 0 0 2 0 1 | 1 0 2 . . x3o . *d3o3o ♦ 5 | 0 10 | 0 0 10 | 0 0 0 5 | * * * * 48 | 0 0 0 2 1 | 0 1 2 -----------------+----+--------+------------+----------------+-------------------+---------------+-------- x3o x3o3o . . ♦ 12 | 12 18 | 4 18 12 | 6 12 3 0 | 4 3 0 0 0 | 40 * * * * | 2 0 0 x3o x3o . *d3o . ♦ 12 | 12 18 | 4 18 12 | 6 12 0 3 | 4 0 3 0 0 | * 80 * * * | 1 1 0 x . x3o3o *d3o . ♦ 16 | 8 48 | 0 24 64 | 0 32 16 16 | 0 8 8 2 0 | * * 30 * * | 1 0 1 x . x3o . *d3o3o ♦ 10 | 5 20 | 0 10 20 | 0 10 0 10 | 0 0 5 0 2 | * * * 48 * | 0 1 1 . . x3o3o *d3o3o ♦ 16 | 0 80 | 0 0 160 | 0 0 40 80 | 0 0 0 10 16 | * * * * 3 | 0 0 2 -----------------+----+--------+------------+----------------+-------------------+---------------+-------- x3o x3o3o *d3o . ♦ 24 | 24 72 | 8 72 96 | 24 96 24 24 | 32 24 24 3 0 | 8 8 3 0 0 | 10 * * x3o x3o . *d3o3o ♦ 15 | 15 30 | 5 30 30 | 10 30 0 15 | 10 0 15 0 3 | 0 5 0 3 0 | * 16 * x . x3o3o *d3o3o ♦ 32 | 16 160 | 0 80 320 | 0 160 80 160 | 0 40 80 20 32 | 0 0 10 16 2 | * * 3
ox xx3oo3oo *c3oo3oo&#x → height = sqrt(3)/2 = 0.866025
(hin || hinnip)
o. o.3o.3o. *c3o.3o. | 16 * | 10 2 0 0 | 30 1 20 0 0 | 10 20 10 60 0 0 0 | 5 5 30 20 40 0 0 0 0 | 1 10 20 5 5 0 0 0 | 5 5 2 0
.o .o3.o3.o *c3.o3.o | * 32 | 0 1 1 10 | 0 1 10 10 30 | 0 0 10 30 30 10 20 | 0 0 30 10 20 10 20 5 5 | 0 10 20 5 5 5 5 1 | 5 5 1 1
------------------------+-------+--------------+-------------------+-------------------------+------------------------------+-----------------------+----------
.. x. .. .. .. .. | 2 0 | 80 * * * | 6 0 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
oo oo3oo3oo *c3oo3oo&#x | 1 1 | * 32 * * | 0 1 10 0 0 | 0 0 10 30 0 0 0 | 0 0 30 10 20 0 0 0 0 | 0 10 20 5 5 0 0 0 | 5 5 1 0
.x .. .. .. .. .. | 0 2 | * * 16 * | 0 1 0 10 0 | 0 0 10 0 30 0 0 | 0 0 30 0 0 10 20 0 0 | 0 10 20 0 0 5 5 0 | 5 5 0 1
.. .x .. .. .. .. | 0 2 | * * * 160 | 0 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.3o. .. .. .. | 3 0 | 3 0 0 0 | 160 * * * * | 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
ox .. .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 16 * * * ♦ 0 0 10 0 0 0 0 | 0 0 30 0 0 0 0 0 0 | 0 10 20 0 0 0 0 0 | 5 5 0 0
.. xx .. .. .. ..&#x | 2 2 | 1 2 0 1 | * * 160 * * | 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 .x .. .. .. .. | 0 4 | 0 0 2 2 | * * * 80 * | 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
.. .x3.o .. .. .. | 0 3 | 0 0 0 3 | * * * * 320 | 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
------------------------+-------+--------------+-------------------+-------------------------+------------------------------+-----------------------+----------
.. x.3o.3o. .. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 40 * * * * * * | 2 0 0 2 0 0 0 0 0 | 1 1 0 4 0 0 0 0 | 2 0 2 0
.. x.3o. .. *c3o. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | * 80 * * * * * | 1 1 0 0 2 0 0 0 0 | 1 0 1 2 2 0 0 0 | 1 1 2 0
ox xx .. .. .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | * * 80 * * * * ♦ 0 0 6 0 0 0 0 0 0 | 0 3 6 0 0 0 0 0 | 3 2 0 0
.. xx3oo .. .. ..&#x ♦ 3 3 | 3 3 0 3 | 1 0 3 0 1 | * * * 320 * * * | 0 0 1 1 2 0 0 0 0 | 0 1 2 2 1 0 0 0 | 2 1 1 0
.x .x3.o .. .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 3 2 | * * * * 160 * * | 0 0 1 0 0 1 2 0 0 | 0 1 2 0 0 2 1 0 | 2 1 0 1
.. .x3.o3.o .. .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * 80 * | 0 0 0 1 0 1 0 2 0 | 0 1 0 2 0 2 0 1 | 2 0 1 1
.. .x3.o .. *c3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * * 160 | 0 0 0 0 1 0 1 1 1 | 0 0 1 1 1 1 1 1 | 1 1 1 1
------------------------+-------+--------------+-------------------+-------------------------+------------------------------+-----------------------+----------
.. x.3o.3o. *c3o. .. ♦ 8 0 | 24 0 0 0 | 32 0 0 0 0 | 8 8 0 0 0 0 0 | 10 * * * * * * * * | 1 0 0 2 0 0 0 0 | 1 0 2 0
.. x.3o. .. *c3o.3o. ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 | 0 5 0 0 0 0 0 | * 16 * * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0
ox xx3oo .. .. ..&#x ♦ 3 6 | 3 6 3 6 | 1 3 6 3 2 | 0 0 3 2 1 0 0 | * * 160 * * * * * * | 0 1 2 0 0 0 0 0 | 2 1 0 0
.. xx3oo3oo .. ..&#x ♦ 4 4 | 6 4 0 6 | 4 0 6 0 4 | 1 0 0 4 0 1 0 | * * * 80 * * * * * | 0 1 0 2 0 0 0 0 | 2 0 1 0
.. xx3oo .. *c3oo ..&#x ♦ 4 4 | 6 4 0 6 | 4 0 6 0 4 | 0 1 0 4 0 0 1 | * * * * 160 * * * * | 0 0 1 1 1 0 0 0 | 1 1 1 0
.x .x3.o3.o .. .. ♦ 0 8 | 0 0 4 12 | 0 0 0 6 8 | 0 0 0 0 4 2 0 | * * * * * 40 * * * | 0 1 0 0 0 2 0 0 | 2 0 0 1
.x .x3.o .. *c3.o .. ♦ 0 8 | 0 0 4 12 | 0 0 0 6 8 | 0 0 0 0 4 0 2 | * * * * * * 80 * * | 0 0 1 0 0 1 1 0 | 1 1 0 1
.. .x3.o3.o *c3.o .. ♦ 0 8 | 0 0 0 24 | 0 0 0 0 32 | 0 0 0 0 0 8 8 | * * * * * * * 20 * | 0 0 0 1 0 1 0 1 | 1 0 1 1
.. .x3.o .. *c3.o3.o ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * * * 32 | 0 0 0 0 1 0 1 1 | 0 1 1 1
------------------------+-------+--------------+-------------------+-------------------------+------------------------------+-----------------------+----------
.. x.3o.3o. *c3o.3o. ♦ 16 0 | 80 0 0 0 | 160 0 0 0 0 | 40 80 0 0 0 0 0 | 10 16 0 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
ox xx3oo3oo .. ..&#x ♦ 4 8 | 6 8 4 12 | 4 4 12 6 8 | 1 0 6 8 4 2 0 | 0 0 4 2 0 1 0 0 0 | * 40 * * * * * * | 2 0 0 0
ox xx3oo .. *c3oo ..&#x ♦ 4 8 | 6 8 4 12 | 4 4 12 6 8 | 0 1 6 8 4 0 2 | 0 0 4 0 2 0 1 0 0 | * * 80 * * * * * | 1 1 0 0
.. xx3oo3oo *c3oo ..&#x ♦ 8 8 | 24 8 0 24 | 32 0 24 0 32 | 8 8 0 32 0 8 8 | 1 0 0 8 8 0 0 1 0 | * * * 20 * * * * | 1 0 1 0
.. xx3oo .. *c3oo3oo&#x ♦ 5 5 | 10 5 0 10 | 10 0 10 0 10 | 0 5 0 10 0 0 5 | 0 1 0 0 5 0 0 0 1 | * * * * 32 * * * | 0 1 1 0
.x .x3.o3.o *c3.o .. ♦ 0 16 | 0 0 8 48 | 0 0 0 24 64 | 0 0 0 0 32 16 16 | 0 0 0 0 0 8 8 2 0 | * * * * * 10 * * | 1 0 0 1
.x .x3.o .. *c3.o3.o ♦ 0 10 | 0 0 5 20 | 0 0 0 10 20 | 0 0 0 0 10 0 10 | 0 0 0 0 0 0 5 0 2 | * * * * * * 16 * | 0 1 0 1
.. .x3.o3.o *c3.o3.o ♦ 0 16 | 0 0 0 80 | 0 0 0 0 160 | 0 0 0 0 0 40 80 | 0 0 0 0 0 0 0 10 16 | * * * * * * * 2 | 0 0 1 1
------------------------+-------+--------------+-------------------+-------------------------+------------------------------+-----------------------+----------
ox xx3oo3oo *c3oo ..&#x ♦ 8 16 | 24 16 8 48 | 32 8 48 24 64 | 8 8 24 64 32 16 16 | 1 0 32 16 16 8 8 2 0 | 0 8 8 2 0 1 0 0 | 10 * * *
ox xx3oo .. *c3oo3oo&#x ♦ 5 10 | 10 10 5 20 | 10 5 20 10 20 | 0 5 10 20 10 0 10 | 0 1 10 0 10 0 5 0 2 | 0 0 5 0 2 0 1 0 | * 16 * *
.. xx3oo3oo *c3oo3oo&#x ♦ 16 16 | 80 16 0 80 | 160 0 80 0 160 | 40 80 0 160 0 40 80 | 10 16 0 40 80 0 0 10 16 | 1 0 0 10 16 0 0 1 | * * 2 *
.x .x3.o3.o *c3.o3.o ♦ 0 32 | 0 0 16 160 | 0 0 0 80 320 | 0 0 0 0 160 80 160 | 0 0 0 0 0 40 80 20 32 | 0 0 0 0 0 10 16 2 | * * * 1
© 2004-2025 | top of page |