| Acronym | trial trapen | ||
| Name |
triangle atop inverted triangle-pentachoron duoprism, triangle-first cap of roc | ||
| Circumradius | sqrt(3)/2 = 0.866025 | ||
|
Lace hyper city in approx. ASCII-art |
| ||
| Face vector | 18, 78, 156, 180, 128, 54, 12 | ||
| Confer |
|
Incidence matrix according to Dynkin symbol
xo3ox ox3oo3oo3oo&#x → height = 2/sqrt(15) = 0.516398
({3} || {3}-dual trapen)
o.3o. o.3o.3o.3o. | 3 * ♦ 2 10 0 0 | 1 10 5 20 0 0 0 | 5 20 10 20 0 0 0 | 10 20 10 10 0 0 0 | 10 10 5 2 0 0 | 5 2 1 0
.o3.o .o3.o3.o3.o | * 15 | 0 2 2 4 | 0 1 2 8 1 8 6 | 1 4 8 12 4 12 4 | 4 6 12 8 6 8 1 | 6 4 8 2 4 2 | 4 1 2 1
---------------------+------+------------+--------------------+---------------------+---------------------+----------------+--------
x. .. .. .. .. .. | 2 0 | 3 * * * | 1 5 0 0 0 0 0 | 5 10 0 0 0 0 0 | 10 10 0 0 0 0 0 | 10 5 0 0 0 0 | 5 1 0 0
oo3oo oo3oo3oo3oo&#x | 1 1 | * 30 * * | 0 1 1 4 0 0 0 | 1 4 4 6 0 0 0 | 4 6 6 4 0 0 0 | 6 4 4 1 0 0 | 4 1 1 0
.. .x .. .. .. .. | 0 2 | * * 15 * | 0 0 1 0 1 4 0 | 1 0 4 0 4 6 0 | 4 0 6 0 6 4 0 | 6 0 4 0 4 1 | 4 0 1 1
.. .. .x .. .. .. | 0 2 | * * * 30 | 0 0 0 2 0 2 3 | 0 1 2 6 1 6 3 | 1 3 6 6 3 6 1 | 3 3 6 2 3 2 | 3 1 2 1
---------------------+------+------------+--------------------+---------------------+---------------------+----------------+--------
x.3o. .. .. .. .. | 3 0 | 3 0 0 0 | 1 * * * * * * ♦ 5 0 0 0 0 0 0 | 10 0 0 0 0 0 0 | 10 0 0 0 0 0 | 5 0 0 0
xo .. .. .. .. ..&#x | 2 1 | 1 2 0 0 | * 15 * * * * * | 1 4 0 0 0 0 0 | 4 6 0 0 0 0 0 | 6 4 0 0 0 0 | 4 1 0 0
.. ox .. .. .. ..&#x | 1 2 | 0 2 1 0 | * * 15 * * * * ♦ 1 0 4 0 0 0 0 | 4 0 6 0 0 0 0 | 6 0 4 0 0 0 | 4 0 1 0
.. .. ox .. .. ..&#x | 1 2 | 0 2 0 1 | * * * 60 * * * | 0 1 1 3 0 0 0 | 1 3 3 3 0 0 0 | 3 3 3 1 0 0 | 3 1 1 0
.o3.x .. .. .. .. | 0 3 | 0 0 3 0 | * * * * 5 * * | 1 0 0 0 4 0 0 | 4 0 0 0 6 0 0 | 6 0 0 0 4 0 | 4 0 0 1
.. .x .x .. .. .. | 0 4 | 0 0 2 2 | * * * * * 30 * | 0 0 1 0 1 3 0 | 1 0 3 0 3 3 0 | 3 0 3 0 3 1 | 3 0 1 1
.. .. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * * * * 30 | 0 0 0 2 0 2 2 | 0 1 2 4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1
---------------------+------+------------+--------------------+---------------------+---------------------+----------------+--------
xo3ox .. .. .. ..&#x ♦ 3 3 | 3 6 3 0 | 1 3 3 0 1 0 0 | 5 * * * * * * ♦ 4 0 0 0 0 0 0 | 6 0 0 0 0 0 | 4 0 0 0
xo .. ox .. .. ..&#x ♦ 2 2 | 1 4 0 1 | 0 2 0 2 0 0 0 | * 30 * * * * * | 1 3 0 0 0 0 0 | 3 3 0 0 0 0 | 3 1 0 0
.. ox ox .. .. ..&#x ♦ 1 4 | 0 4 2 2 | 0 0 2 2 0 1 0 | * * 30 * * * * ♦ 1 0 3 0 0 0 0 | 3 0 3 0 0 0 | 3 0 1 0
.. .. ox3oo .. ..&#x ♦ 1 3 | 0 3 0 3 | 0 0 0 3 0 0 1 | * * * 60 * * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0
.o3.x .x .. .. .. ♦ 0 6 | 0 0 6 3 | 0 0 0 0 2 3 0 | * * * * 10 * * | 1 0 0 0 3 0 0 | 3 0 0 0 3 0 | 3 0 0 1
.. .x .x3.o .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * 30 * | 0 0 1 0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1
.. .. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * 15 | 0 0 0 2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1
---------------------+------+------------+--------------------+---------------------+---------------------+----------------+--------
xo3ox ox .. .. ..&#x ♦ 3 6 | 3 12 6 3 | 1 6 6 6 2 3 0 | 2 3 3 0 1 0 0 | 10 * * * * * * | 3 0 0 0 0 0 | 3 0 0 0
xo .. ox3oo .. ..&#x ♦ 2 3 | 1 6 0 3 | 0 3 0 6 0 0 1 | 0 3 0 2 0 0 0 | * 30 * * * * * | 1 2 0 0 0 0 | 2 1 0 0
.. ox ox3oo .. ..&#x ♦ 1 6 | 0 6 3 6 | 0 0 3 6 0 3 2 | 0 0 3 2 0 1 0 | * * 30 * * * * | 1 0 2 0 0 0 | 2 0 1 0
.. .. ox3oo3oo ..&#x ♦ 1 4 | 0 4 0 6 | 0 0 0 6 0 0 4 | 0 0 0 4 0 0 1 | * * * 30 * * * | 0 1 1 1 0 0 | 1 1 1 0
.o3.x .x3.o .. .. ♦ 0 9 | 0 0 9 9 | 0 0 0 0 3 9 3 | 0 0 0 0 3 3 0 | * * * * 10 * * | 1 0 0 0 2 0 | 2 0 0 1
.. .x .x3.o3.o .. ♦ 0 8 | 0 0 4 12 | 0 0 0 0 0 6 8 | 0 0 0 0 0 4 2 | * * * * * 15 * | 0 0 1 0 1 1 | 1 0 1 1
.. .. .x3.o3.o3.o ♦ 0 5 | 0 0 0 10 | 0 0 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * 3 | 0 0 0 2 0 2 | 0 1 2 1
---------------------+------+------------+--------------------+---------------------+---------------------+----------------+--------
xo3ox ox3oo .. ..&#x ♦ 3 9 | 3 18 9 9 | 1 9 9 18 3 9 3 | 3 9 9 6 3 3 0 | 3 3 3 0 1 0 0 | 10 * * * * * | 2 0 0 0
xo .. ox3oo3oo ..&#x ♦ 2 4 | 1 8 0 6 | 0 4 0 12 0 0 4 | 0 6 0 8 0 0 1 | 0 4 0 2 0 0 0 | * 15 * * * * | 1 1 0 0
.. ox ox3oo3oo ..&#x ♦ 1 8 | 0 8 4 12 | 0 0 4 12 0 6 8 | 0 0 6 8 0 4 2 | 0 0 4 2 0 1 0 | * * 15 * * * | 1 0 1 0
.. .. ox3oo3oo3oo&#x ♦ 1 5 | 0 5 0 10 | 0 0 0 10 0 0 10 | 0 0 0 10 0 0 5 | 0 0 0 5 0 0 1 | * * * 6 * * | 0 1 1 0
.o3.x .x3.o3.o .. ♦ 0 12 | 0 0 12 18 | 0 0 0 0 4 18 12 | 0 0 0 0 6 12 3 | 0 0 0 0 4 3 0 | * * * * 5 * | 1 0 0 1
.. .x .x3.o3.o3.o ♦ 0 10 | 0 0 5 20 | 0 0 0 0 0 10 20 | 0 0 0 0 0 10 10 | 0 0 0 0 0 5 2 | * * * * * 3 | 0 0 1 1
---------------------+------+------------+--------------------+---------------------+---------------------+----------------+--------
xo3ox ox3oo3oo ..&#x ♦ 3 12 | 3 24 12 18 | 1 12 12 36 4 18 12 | 4 18 18 24 6 12 3 | 6 12 12 6 4 3 0 | 4 3 3 0 1 0 | 5 * * *
xo .. ox3oo3oo3oo&#x ♦ 2 5 | 1 10 0 10 | 0 5 0 20 0 0 10 | 0 10 0 20 0 0 5 | 0 10 0 10 0 0 1 | 0 5 0 2 0 0 | * 3 * *
.. ox ox3oo3oo3oo&#x ♦ 1 10 | 0 10 5 20 | 0 0 5 20 0 10 20 | 0 0 10 20 0 10 10 | 0 0 10 10 0 5 2 | 0 0 5 2 0 1 | * * 3 *
.o3.x .x3.o3.o3.o ♦ 0 15 | 0 0 15 30 | 0 0 0 0 5 30 30 | 0 0 0 0 10 30 15 | 0 0 0 0 10 15 3 | 0 0 0 0 5 3 | * * * 1
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