vertex pyramid of the dodecateron
- uniform relative:
- dot
- general polytopal classes:
- segmentotera lace simplices
links
| Acronym | triddippy |
| Name |
trigonal-duoprismatic pyramid, vertex pyramid of the dodecateron |
| Circumradius | sqrt(3)/2 = 0.866025 |
| Face vector | 10, 27, 33, 21, 7 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
ox3oo ox3oo&#x → height = 1/sqrt(3) = 0.577350
(pt || triddip)
o.3o. o.3o. | 1 * ♦ 9 0 0 | 9 9 0 0 0 | 3 9 3 0 0 | 3 3 0
.o3.o .o3.o | * 9 | 1 2 2 | 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
---------------+-----+-------+-----------+-----------+------
oo3oo oo3oo&#x | 1 1 | 9 * * ♦ 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x .. .. .. | 0 2 | * 9 * | 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x .. | 0 2 | * * 9 | 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
---------------+-----+-------+-----------+-----------+------
ox .. .. ..&#x | 1 2 | 2 1 0 | 9 * * * * | 1 2 0 0 0 | 2 1 0
.. .. ox ..&#x | 1 2 | 2 0 1 | * 9 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .. .. | 0 3 | 0 3 0 | * * 3 * * | 1 0 0 2 0 | 2 0 1
.x .. .x .. | 0 4 | 0 2 2 | * * * 9 * | 0 1 0 1 1 | 1 1 1
.. .. .x3.o | 0 3 | 0 0 3 | * * * * 3 | 0 0 1 0 2 | 0 2 1
---------------+-----+-------+-----------+-----------+------
ox3oo .. ..&#x ♦ 1 3 | 3 3 0 | 3 0 1 0 0 | 3 * * * * | 2 0 0
ox .. ox ..&#x ♦ 1 4 | 4 2 2 | 2 2 0 1 0 | * 9 * * * | 1 1 0
.. .. ox3oo&#x ♦ 1 3 | 3 0 3 | 0 3 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x .. ♦ 0 6 | 0 6 3 | 0 0 2 3 0 | * * * 3 * | 1 0 1
.x .. .x3.o ♦ 0 6 | 0 3 6 | 0 0 0 3 2 | * * * * 3 | 0 1 1
---------------+-----+-------+-----------+-----------+------
ox3oo ox ..&#x ♦ 1 6 | 6 6 3 | 6 3 2 3 0 | 2 3 0 1 0 | 3 * *
ox .. ox3oo&#x ♦ 1 6 | 6 3 6 | 3 6 0 3 2 | 0 3 2 0 1 | * 3 *
.x3.o .x3.o ♦ 0 9 | 0 9 9 | 0 0 3 9 3 | 0 0 0 3 3 | * * 1
or o.3o. o.3o. | 1 * ♦ 9 0 | 18 0 0 | 6 9 0 | 6 0 .o3.o .o3.o | * 9 | 1 4 | 4 2 4 | 2 4 4 | 4 1 -----------------+-----+------+--------+-------+---- oo3oo oo3oo&#x | 1 1 | 9 * ♦ 4 0 0 | 2 4 0 | 4 0 .x .. .. .. & | 0 2 | * 18 | 1 1 2 | 1 2 3 | 3 1 -----------------+-----+------+--------+-------+---- ox .. .. ..&#x & | 1 2 | 2 1 | 18 * * | 1 2 0 | 3 0 .x3.o .. .. & | 0 3 | 0 3 | * 6 * | 1 0 2 | 2 1 .x .. .x .. | 0 4 | 0 4 | * * 9 | 0 1 2 | 2 1 -----------------+-----+------+--------+-------+---- ox3oo .. ..&#x & ♦ 1 3 | 3 3 | 3 1 0 | 6 * * | 2 0 ox .. ox ..&#x ♦ 1 4 | 4 4 | 4 0 1 | * 9 * | 2 0 .x3.o .x .. & ♦ 0 6 | 0 9 | 0 2 3 | * * 6 | 1 1 -----------------+-----+------+--------+-------+---- ox3oo ox ..&#x & ♦ 1 6 | 6 9 | 9 2 3 | 2 3 1 | 6 * .x3.o .x3.o ♦ 0 9 | 0 18 | 0 6 9 | 0 0 6 | * 1
oox ooo3oxx&#x → height(1,2) = sqrt(2/3) = 0.816497
height(1,3) = sqrt(5/12) = 0.645497
height(2,3) = sqrt(3)/2 = 0.866025
o.. o..3o.. | 1 * * ♦ 3 6 0 0 0 0 | 3 3 6 6 0 0 0 0 0 | 1 3 2 3 6 0 0 0 | 1 3 2 0
.o. .o.3.o. | * 3 * | 1 0 2 2 0 0 | 2 0 0 2 1 1 4 0 0 | 1 0 0 1 4 2 2 0 | 0 2 2 1
..o ..o3..o | * * 6 | 0 1 0 1 1 2 | 0 1 2 1 0 1 2 2 1 | 0 2 1 1 2 2 1 1 | 1 2 1 1
---------------+-------+-------------+-------------------+-----------------+--------
oo. oo.3oo.&#x | 1 1 0 | 3 * * * * * ♦ 2 0 0 2 0 0 0 0 0 | 1 0 0 1 4 0 0 0 | 0 2 2 0
o.o o.o3o.o&#x | 1 0 1 | * 6 * * * * ♦ 0 1 2 2 0 0 0 0 0 | 0 2 1 1 2 0 0 0 | 1 2 1 0
... ... .x. | 0 2 0 | * * 3 * * * | 1 0 0 0 1 0 2 0 0 | 1 0 0 0 2 1 2 0 | 0 1 2 1
.oo .oo3.oo&#x | 0 1 1 | * * * 6 * * | 0 0 0 1 0 1 2 0 0 | 0 0 0 1 2 2 1 0 | 0 2 1 1
..x ... ... | 0 0 2 | * * * * 3 * | 0 1 0 0 0 1 0 2 0 | 0 2 0 1 0 2 0 1 | 1 2 0 1
... ... ..x | 0 0 2 | * * * * * 6 | 0 0 1 0 0 0 1 1 1 | 0 1 1 0 1 1 1 1 | 1 1 1 1
---------------+-------+-------------+-------------------+-----------------+--------
... ... ox.&#x | 1 2 0 | 2 0 1 0 0 0 | 3 * * * * * * * * | 1 0 0 0 2 0 0 0 | 0 1 2 0
o.x ... ...&#x | 1 0 2 | 0 2 0 0 1 0 | * 3 * * * * * * * | 0 2 0 1 0 0 0 0 | 1 2 0 0
... ... o.x&#x | 1 0 2 | 0 2 0 0 0 1 | * * 6 * * * * * * | 0 1 1 0 1 0 0 0 | 1 1 1 0
ooo ooo3ooo&#x | 1 1 1 | 1 1 0 1 0 0 | * * * 6 * * * * * | 0 0 0 1 2 0 0 0 | 0 2 1 0
... .o.3.x. | 0 3 0 | 0 0 3 0 0 0 | * * * * 1 * * * * | 1 0 0 0 0 0 2 0 | 0 0 2 1
.ox ... ...&#x | 0 1 2 | 0 0 0 2 1 0 | * * * * * 3 * * * | 0 0 0 1 0 2 0 0 | 0 2 0 1
... ... .xx&#x | 0 2 2 | 0 0 1 2 0 1 | * * * * * * 6 * * | 0 0 0 0 1 1 1 0 | 0 1 1 1
..x ... ..x | 0 0 4 | 0 0 0 0 2 2 | * * * * * * * 3 * | 0 1 0 0 0 1 0 1 | 1 1 0 1
... ..o3..x | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 2 | 0 0 1 0 0 0 1 1 | 1 0 1 1
---------------+-------+-------------+-------------------+-----------------+--------
... oo.3ox.&#x ♦ 1 3 0 | 3 0 3 0 0 0 | 3 0 0 0 1 0 0 0 0 | 1 * * * * * * * | 0 0 2 0
o.x ... o.x&#x ♦ 1 0 4 | 0 4 0 0 2 2 | 0 2 2 0 0 0 0 1 0 | * 3 * * * * * * | 1 1 0 0
... o.o3o.x&#x ♦ 1 0 3 | 0 3 0 0 0 3 | 0 0 3 0 0 0 0 0 1 | * * 2 * * * * * | 1 0 1 0
oox ... ...&#x ♦ 1 1 2 | 1 2 0 2 1 0 | 0 1 0 2 0 1 0 0 0 | * * * 3 * * * * | 0 2 0 0
... ... oxx&#x ♦ 1 2 2 | 2 2 1 2 0 1 | 1 0 1 2 0 0 1 0 0 | * * * * 6 * * * | 0 1 1 0
.ox ... .xx&#x ♦ 0 2 4 | 0 0 1 4 2 2 | 0 0 0 0 0 2 2 1 0 | * * * * * 3 * * | 0 1 0 1
... .oo3.xx&#x ♦ 0 3 3 | 0 0 3 3 0 3 | 0 0 0 0 1 0 3 0 1 | * * * * * * 2 * | 0 0 1 1
..x ..o3..x ♦ 0 0 6 | 0 0 0 0 3 6 | 0 0 0 0 0 0 0 3 2 | * * * * * * * 1 | 1 0 0 1
---------------+-------+-------------+-------------------+-----------------+--------
o.x o.o3o.x&#x ♦ 1 0 6 | 0 6 0 0 3 6 | 0 3 6 0 0 0 0 3 2 | 0 3 2 0 0 0 0 1 | 1 * * *
oox ... oxx&#x ♦ 1 2 4 | 2 4 1 4 2 2 | 1 2 2 4 0 2 2 1 0 | 0 1 0 2 2 1 0 0 | * 3 * *
... ooo3oxx&#x ♦ 1 3 3 | 3 3 3 3 0 3 | 3 0 3 3 1 0 3 0 1 | 1 0 1 0 3 0 1 0 | * * 2 *
.ox .oo3.xx&#x ♦ 0 3 6 | 0 0 3 6 3 6 | 0 0 0 0 1 3 6 3 2 | 0 0 0 0 0 3 2 1 | * * * 1
oooo3oxxx&#x → height(1,2) = height(1,3) = height(1,4) = sqrt(2/3) = 0.816497
height(2,3) = height(2,4) = height(3,4) = 1
o...3o... | 1 * * * ♦ 3 3 3 0 0 0 0 0 0 | 3 3 3 3 3 3 0 0 0 0 0 0 0 | 1 3 3 3 1 3 1 0 0 0 0 | 1 3 1 1 0
.o..3.o.. | * 3 * * | 1 0 0 2 1 1 0 0 0 | 2 1 1 0 0 0 1 2 1 2 0 0 0 | 1 2 1 2 0 0 0 1 2 1 0 | 1 2 1 0 1
..o.3..o. | * * 3 * | 0 1 0 0 1 0 2 1 0 | 0 1 0 2 1 0 0 2 1 0 1 2 0 | 0 2 1 0 1 2 0 1 2 0 1 | 1 2 0 1 1
...o3...o | * * * 3 | 0 0 1 0 0 1 0 1 2 | 0 0 1 0 1 2 0 0 1 2 0 2 1 | 0 0 1 2 0 2 1 0 2 1 1 | 0 2 1 1 1
-------------+---------+-------------------+---------------------------+-----------------------+----------
oo..3oo..&#x | 1 1 0 0 | 3 * * * * * * * * ♦ 2 1 1 0 0 0 0 0 0 0 0 0 0 | 1 2 1 2 0 0 0 0 0 0 0 | 1 2 1 0 0
o.o.3o.o.&#x | 1 0 1 0 | * 3 * * * * * * * ♦ 0 1 0 2 1 0 0 0 0 0 0 0 0 | 0 2 1 0 1 2 0 0 0 0 0 | 1 2 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * 3 * * * * * * ♦ 0 0 1 0 1 2 0 0 0 0 0 0 0 | 0 0 1 2 0 2 1 0 0 0 0 | 0 2 1 1 0
.... .x.. | 0 2 0 0 | * * * 3 * * * * * | 1 0 0 0 0 0 1 1 0 1 0 0 0 | 1 1 0 1 0 0 0 1 1 1 0 | 1 1 1 0 1
.oo.3.oo.&#x | 0 1 1 0 | * * * * 3 * * * * | 0 1 0 0 0 0 0 2 1 0 0 0 0 | 0 2 1 0 0 0 0 1 2 0 0 | 1 2 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * * 3 * * * | 0 0 1 0 0 0 0 0 1 2 0 0 0 | 0 0 1 2 0 0 0 0 2 1 0 | 0 2 1 0 1
.... ..x. | 0 0 2 0 | * * * * * * 3 * * | 0 0 0 1 0 0 0 1 0 0 1 1 0 | 0 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * 3 * | 0 0 0 0 1 0 0 0 1 0 0 2 0 | 0 0 1 0 0 2 0 0 2 0 1 | 0 2 0 1 1
.... ...x | 0 0 0 2 | * * * * * * * * 3 | 0 0 0 0 0 1 0 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
-------------+---------+-------------------+---------------------------+-----------------------+----------
.... ox..&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 0 | 3 * * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0
ooo.3ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | * 3 * * * * * * * * * * * | 0 2 1 0 0 0 0 0 0 0 0 | 1 2 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * * 3 * * * * * * * * * * | 0 0 1 2 0 0 0 0 0 0 0 | 0 2 1 0 0
.... o.x.&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 | * * * 3 * * * * * * * * * | 0 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
o.oo3o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * * * 3 * * * * * * * * | 0 0 1 0 0 2 0 0 0 0 0 | 0 2 0 1 0
.... o..x&#x | 1 0 0 2 | 0 0 2 0 0 0 0 0 1 | * * * * * 3 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.o..3.x.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 | * * * * * * 1 * * * * * * | 1 0 0 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.... .xx.&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * * * * * 3 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * * * * 3 * * * * | 0 0 1 0 0 0 0 0 2 0 0 | 0 2 0 0 1
.... .x.x&#x | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 | * * * * * * * * * 3 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
..o.3..x. | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * 1 * * | 0 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
.... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * 3 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
...o3...x | 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * 1 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
-------------+---------+-------------------+---------------------------+-----------------------+----------
oo..3ox..&#x ♦ 1 3 0 0 | 3 0 0 3 0 0 0 0 0 | 3 0 0 0 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 0 1 0 0
.... oxx.&#x ♦ 1 2 2 0 | 2 2 0 1 2 0 1 0 0 | 1 2 0 1 0 0 0 1 0 0 0 0 0 | * 3 * * * * * * * * * | 1 1 0 0 0
oooo3oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 0 1 1 0 1 0 0 0 1 0 0 0 0 | * * 3 * * * * * * * * | 0 2 0 0 0
.... ox.x&#x ♦ 1 2 0 2 | 2 0 2 1 0 2 0 0 1 | 1 0 2 0 0 1 0 0 0 1 0 0 0 | * * * 3 * * * * * * * | 0 1 1 0 0
o.o.3o.x.&#x ♦ 1 0 3 0 | 0 3 0 0 0 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 1 0 0 | * * * * 1 * * * * * * | 1 0 0 1 0
.... o.xx&#x ♦ 1 0 2 2 | 0 2 2 0 0 0 1 2 1 | 0 0 0 1 2 1 0 0 0 0 0 1 0 | * * * * * 3 * * * * * | 0 1 0 1 0
o..o3o..x&#x ♦ 1 0 0 3 | 0 0 3 0 0 0 0 0 3 | 0 0 0 0 0 3 0 0 0 0 0 0 1 | * * * * * * 1 * * * * | 0 0 1 1 0
.oo.3.xx.&#x ♦ 0 3 3 0 | 0 0 0 3 3 0 3 0 0 | 0 0 0 0 0 0 1 3 0 0 1 0 0 | * * * * * * * 1 * * * | 1 0 0 0 1
.... .xxx&#x ♦ 0 2 2 2 | 0 0 0 1 2 2 1 2 1 | 0 0 0 0 0 0 0 1 2 1 0 1 0 | * * * * * * * * 3 * * | 0 1 0 0 1
.o.o3.x.x&#x ♦ 0 3 0 3 | 0 0 0 3 0 3 0 0 3 | 0 0 0 0 0 0 1 0 0 3 0 0 1 | * * * * * * * * * 1 * | 0 0 1 0 1
..oo3..xx&#x ♦ 0 0 3 3 | 0 0 0 0 0 0 3 3 3 | 0 0 0 0 0 0 0 0 0 0 1 3 1 | * * * * * * * * * * 1 | 0 0 0 1 1
-------------+---------+-------------------+---------------------------+-----------------------+----------
ooo.3oxx.&#x ♦ 1 3 3 0 | 3 3 0 3 3 0 3 0 0 | 3 3 0 3 0 0 1 3 0 0 1 0 0 | 1 3 0 0 1 0 0 1 0 0 0 | 1 * * * *
.... oxxx&#x ♦ 1 2 2 2 | 2 2 2 1 2 2 1 2 1 | 1 2 2 1 2 1 0 1 2 1 0 1 0 | 0 1 2 1 0 1 0 0 1 0 0 | * 3 * * *
oo.o3ox.x&#x ♦ 1 3 0 3 | 3 0 3 3 0 3 0 0 3 | 3 0 3 0 0 3 1 0 0 3 0 0 1 | 1 0 0 3 0 0 1 0 0 1 0 | * * 1 * *
o.oo3o.xx&#x ♦ 1 0 3 3 | 0 3 3 0 0 0 3 3 3 | 0 0 0 3 3 3 0 0 0 0 1 3 1 | 0 0 0 0 1 3 1 0 0 0 1 | * * * 1 *
.ooo3.xxx&#x ♦ 0 3 3 3 | 0 0 0 3 3 3 3 3 3 | 0 0 0 0 0 0 1 3 3 3 1 3 1 | 0 0 0 0 0 0 0 1 3 1 1 | * * * * 1
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