- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices
links
| Acronym | tippip |
| Name | truncated-pentachoron prism |
| Circumradius | sqrt(37/20) = 1.360147 |
| Volume | 19 sqrt(5)/24 = 1.770220 |
| Face vector | 40, 100, 100, 50, 12 |
| Confer |
|
|
External links |
|
Incidence matrix according to Dynkin symbol
x x3x3o3o . . . . . | 40 | 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 ----------+----+----------+-------------+-------------+------ x . . . . | 2 | 20 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . x . . . | 2 | * 20 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 . . x . . | 2 | * * 60 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+----------+-------------+-------------+------ x x . . . | 4 | 2 2 0 | 10 * * * | 3 0 0 0 | 3 0 0 x . x . . | 4 | 2 0 2 | * 30 * * | 1 2 0 0 | 2 1 0 . x3x . . | 6 | 0 3 3 | * * 20 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 0 3 | * * * 40 | 0 1 1 1 | 1 1 1 ----------+----+----------+-------------+-------------+------ x x3x . . ♦ 12 | 6 6 6 | 3 3 2 0 | 10 * * * | 2 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 | * 20 * * | 1 1 0 . x3x3o . ♦ 12 | 0 6 12 | 0 0 4 4 | * * 10 * | 1 0 1 . . x3o3o ♦ 4 | 0 0 6 | 0 0 0 4 | * * * 10 | 0 1 1 ----------+----+----------+-------------+-------------+------ x x3x3o . ♦ 24 | 12 12 24 | 6 12 8 8 | 4 4 2 0 | 5 * * x . x3o3o ♦ 8 | 4 0 12 | 0 6 0 8 | 0 4 0 2 | * 5 * . x3x3o3o ♦ 20 | 0 10 30 | 0 0 10 20 | 0 0 5 5 | * * 2
xx3xx3oo3oo&#x → height = 1
(tip || tip)
o.3o.3o.3o. | 20 * | 1 3 1 0 0 | 3 3 1 3 0 0 | 3 1 3 3 0 0 | 1 3 1 0
.o3.o3.o3.o | * 20 | 0 0 1 1 3 | 0 0 1 3 3 3 | 0 0 3 3 3 1 | 0 3 1 1
---------------+-------+----------------+-------------------+---------------+--------
x. .. .. .. | 2 0 | 10 * * * * | 3 0 1 0 0 0 | 3 0 3 0 0 0 | 1 3 0 0
.. x. .. .. | 2 0 | * 30 * * * | 1 2 0 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
oo3oo3oo3oo&#x | 1 1 | * * 20 * * | 0 0 1 3 0 0 | 0 0 3 3 0 0 | 0 3 1 0
.x .. .. .. | 0 2 | * * * 10 * | 0 0 1 0 3 0 | 0 0 3 0 3 0 | 0 3 0 1
.. .x .. .. | 0 2 | * * * * 30 | 0 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
---------------+-------+----------------+-------------------+---------------+--------
x.3x. .. .. | 6 0 | 3 3 0 0 0 | 10 * * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x.3o. .. | 3 0 | 0 3 0 0 0 | * 20 * * * * | 1 1 0 1 0 0 | 1 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * 10 * * * | 0 0 3 0 0 0 | 0 3 0 0
.. xx .. ..&#x | 2 2 | 0 1 2 0 1 | * * * 30 * * | 0 0 1 2 0 0 | 0 2 1 0
.x3.x .. .. | 0 6 | 0 0 0 3 3 | * * * * 10 * | 0 0 1 0 2 0 | 0 2 0 1
.. .x3.o .. | 0 3 | 0 0 0 0 3 | * * * * * 20 | 0 0 0 1 1 1 | 0 1 1 1
---------------+-------+----------------+-------------------+---------------+--------
x.3x.3o. .. ♦ 12 0 | 6 12 0 0 0 | 4 4 0 0 0 0 | 5 * * * * * | 1 1 0 0
.. x.3o.3o. ♦ 4 0 | 0 6 0 0 0 | 0 4 0 0 0 0 | * 5 * * * * | 1 0 1 0
xx3xx .. ..&#x ♦ 6 6 | 3 3 6 3 3 | 1 0 3 3 1 0 | * * 10 * * * | 0 2 0 0
.. xx3oo ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 3 0 1 | * * * 20 * * | 0 1 1 0
.x3.x3.o .. ♦ 0 12 | 0 0 0 6 12 | 0 0 0 0 4 4 | * * * * 5 * | 0 1 0 1
.. .x3.o3.o ♦ 0 4 | 0 0 0 0 6 | 0 0 0 0 0 4 | * * * * * 5 | 0 0 1 1
---------------+-------+----------------+-------------------+---------------+--------
x.3x.3o.3o. ♦ 20 0 | 10 30 0 0 0 | 10 20 0 0 0 0 | 5 5 0 0 0 0 | 1 * * *
xx3xx3oo ..&#x ♦ 12 12 | 6 12 12 6 12 | 4 4 6 12 4 4 | 1 0 4 4 1 0 | * 5 * *
.. xx3oo3oo&#x ♦ 4 4 | 0 6 4 0 6 | 0 4 0 6 0 4 | 0 1 0 4 0 1 | * * 5 *
.x3.x3.o3.o ♦ 0 20 | 0 0 0 10 30 | 0 0 0 0 10 20 | 0 0 0 0 5 5 | * * * 1
xxx xux3oox3ooo&#xt → both heights = sqrt(5/8) = 0.790569 o.. o..3o..3o.. | 8 * * | 1 3 1 0 0 0 0 0 | 3 3 1 3 0 0 0 0 0 0 | 3 1 3 3 0 0 0 0 0 | 1 3 1 0 0 .o. .o.3.o.3.o. | * 8 * | 0 0 1 1 3 0 0 0 | 0 0 1 3 3 3 0 0 0 0 | 0 0 3 3 3 1 0 0 0 | 0 3 1 1 0 ..o ..o3..o3..o | * * 24 | 0 0 0 0 1 1 1 2 | 0 0 0 1 1 2 1 2 2 1 | 0 0 1 2 2 1 2 1 1 | 0 2 1 1 1 --------------------+--------+----------------------+-------------------------+--------------------+---------- x.. ... ... ... | 2 0 0 | 4 * * * * * * * | 3 0 1 0 0 0 0 0 0 0 | 3 0 3 0 0 0 0 0 0 | 1 3 0 0 0 ... x.. ... ... | 2 0 0 | * 12 * * * * * * | 1 2 0 1 0 0 0 0 0 0 | 2 1 1 2 0 0 0 0 0 | 1 2 1 0 0 oo. oo.3oo.3oo.&#x | 1 1 0 | * * 8 * * * * * | 0 0 1 3 0 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 | 0 3 1 0 0 .x. ... ... ... | 0 2 0 | * * * 4 * * * * | 0 0 1 0 3 0 0 0 0 0 | 0 0 3 0 3 0 0 0 0 | 0 3 0 1 0 .oo .oo3.oo3.oo&#x | 0 1 1 | * * * * 24 * * * | 0 0 0 1 1 2 0 0 0 0 | 0 0 1 2 2 1 0 0 0 | 0 2 1 1 0 ..x ... ... ... | 0 0 2 | * * * * * 12 * * | 0 0 0 0 1 0 1 2 0 0 | 0 0 1 0 2 0 2 1 0 | 0 2 0 1 1 ... ..x ... ... | 0 0 2 | * * * * * * 12 * | 0 0 0 1 0 0 1 0 2 0 | 0 0 1 2 0 0 2 0 1 | 0 2 1 0 1 ... ... ..x ... | 0 0 2 | * * * * * * * 24 | 0 0 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1 --------------------+--------+----------------------+-------------------------+--------------------+---------- x.. x.. ... ... | 4 0 0 | 2 2 0 0 0 0 0 0 | 6 * * * * * * * * * | 2 0 1 0 0 0 0 0 0 | 1 2 0 0 0 ... x..3o.. ... | 3 0 0 | 0 3 0 0 0 0 0 0 | * 8 * * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0 xx. ... ... ...&#x | 2 2 0 | 1 0 2 1 0 0 0 0 | * * 4 * * * * * * * | 0 0 3 0 0 0 0 0 0 | 0 3 0 0 0 ... xux ... ...&#xt | 2 2 2 | 0 1 2 0 2 0 1 0 | * * * 12 * * * * * * | 0 0 1 2 0 0 0 0 0 | 0 2 1 0 0 .xx ... ... ...&#x | 0 2 2 | 0 0 0 1 2 1 0 0 | * * * * 12 * * * * * | 0 0 1 0 2 0 0 0 0 | 0 2 0 1 0 ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 2 0 0 1 | * * * * * 24 * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 ..x ..x ... ... | 0 0 4 | 0 0 0 0 0 2 2 0 | * * * * * * 6 * * * | 0 0 1 0 0 0 2 0 0 | 0 2 0 0 1 ..x ... ..x ... | 0 0 4 | 0 0 0 0 0 2 0 2 | * * * * * * * 12 * * | 0 0 0 0 1 0 1 1 0 | 0 1 0 1 1 ... ..x3..x ... | 0 0 6 | 0 0 0 0 0 0 3 3 | * * * * * * * * 8 * | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1 ... ... ..x3..o | 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * 8 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1 --------------------+--------+----------------------+-------------------------+--------------------+---------- x.. x..3o.. ... ♦ 6 0 0 | 3 6 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 ... x..3o..3o.. ♦ 4 0 0 | 0 6 0 0 0 0 0 0 | 0 4 0 0 0 0 0 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0 xxx xux ... ...&#xt ♦ 4 4 4 | 2 2 4 2 4 2 2 0 | 1 0 2 2 2 0 1 0 0 0 | * * 6 * * * * * * | 0 2 0 0 0 ... xux3oox ...&#xt ♦ 3 3 6 | 0 3 3 0 6 0 3 3 | 0 1 0 3 0 3 0 0 1 0 | * * * 8 * * * * * | 0 1 1 0 0 .xx ... .ox ...&#x ♦ 0 2 4 | 0 0 0 1 4 2 0 2 | 0 0 0 0 2 2 0 1 0 0 | * * * * 12 * * * * | 0 1 0 1 0 ... ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 0 3 0 0 3 | 0 0 0 0 0 3 0 0 0 1 | * * * * * 8 * * * | 0 0 1 1 0 ..x ..x3..x ... ♦ 0 0 12 | 0 0 0 0 0 6 6 6 | 0 0 0 0 0 0 3 3 2 0 | * * * * * * 4 * * | 0 1 0 0 1 ..x ... ..x3..o ♦ 0 0 6 | 0 0 0 0 0 3 0 6 | 0 0 0 0 0 0 0 3 0 2 | * * * * * * * 4 * | 0 0 0 1 1 ... ..x3..x3..o ♦ 0 0 12 | 0 0 0 0 0 0 6 12 | 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * 2 | 0 0 1 0 1 --------------------+--------+----------------------+-------------------------+--------------------+---------- x.. x..3o..3o.. ♦ 8 0 0 | 4 12 0 0 0 0 0 0 | 6 8 0 0 0 0 0 0 0 0 | 4 2 0 0 0 0 0 0 0 | 1 * * * * xxx xux3oox ...&#xt ♦ 6 6 12 | 3 6 6 3 12 6 6 6 | 3 2 3 6 6 6 3 3 2 0 | 1 0 3 2 3 0 1 0 0 | * 4 * * * ... xux3oox3ooo&#xt ♦ 4 4 12 | 0 6 4 0 12 0 6 12 | 0 4 0 6 0 12 0 0 4 4 | 0 1 0 4 0 4 0 0 1 | * * 2 * * .xx ... .ox3.oo&#x ♦ 0 2 6 | 0 0 0 1 6 3 0 6 | 0 0 0 0 3 6 0 3 0 2 | 0 0 0 0 3 2 0 1 0 | * * * 4 * ..x ..x3..x3..o ♦ 0 0 24 | 0 0 0 0 0 12 12 24 | 0 0 0 0 0 0 6 12 8 8 | 0 0 0 0 0 0 4 4 2 | * * * * 1
© 2004-2024 | top of page |