| Acronym | hixacube |
| Name | hix atop edge-parallel cube |
| Circumradius | sqrt(3)/2 = 0.866025 |
|
Lace hyper city in approx. ASCII-art |
o x o o o x
x o o
x x x
I.e. a regular tetrahedron in position space of 3 mutually orthogonal lines resp. their Minkowski sum (a cube) within object space.
|
| Face vector | 14, 51, 86, 78, 39, 10 |
| Confer |
|
Incidence matrix according to Dynkin symbol
xoox oxox ooxx&#x → all pairwise heights = 1/sqrt(2) = 0.707107
height(123,4) = 1/sqrt(3) = 0.577350
(hix || edge-para cube)
o... o... o... & | 6 * | 1 4 4 0 | 6 4 4 4 8 0 | 2 8 4 1 4 12 4 0 | 5 1 8 4 6 | 1 2 5
...o ...o ...o | * 8 | 0 0 3 3 | 0 0 3 6 3 3 | 0 0 6 3 1 6 3 1 | 0 3 3 3 6 | 0 3 3
--------------------+-----+------------+-----------------+---------------------+-------------+------
x... .... .... & | 2 0 | 3 * * * | 4 0 4 0 0 0 | 2 4 4 0 0 8 0 0 | 4 1 4 4 4 | 1 2 4
oo.. oo.. oo..&#x & | 2 0 | * 12 * * | 2 2 0 0 2 0 | 1 5 0 0 2 4 1 0 | 4 0 5 2 2 | 1 1 4
o..o o..o o..o&#x & | 1 1 | * * 24 * | 0 0 1 2 2 0 | 0 0 2 1 1 4 2 0 | 0 1 3 2 4 | 0 2 3
...x .... .... & | 0 2 | * * * 12 | 0 0 1 2 0 2 | 0 0 4 2 0 2 1 1 | 0 3 1 2 4 | 0 3 2
--------------------+-----+------------+-----------------+---------------------+-------------+------
xo.. .... ....&#x & | 3 0 | 1 2 0 0 | 12 * * * * * | 1 2 0 0 0 2 0 0 | 3 0 2 2 1 | 1 1 3
ooo. ooo. ooo.&#x | 3 0 | 0 3 0 0 | * 8 * * * * | 0 3 0 0 1 0 0 0 | 3 0 3 0 0 | 1 0 3
x..x .... ....&#x & | 2 2 | 1 0 2 1 | * * 12 * * * | 0 0 2 0 0 2 0 0 | 0 1 1 2 2 | 0 2 2
.... o..x ....&#x & | 1 2 | 0 0 2 1 | * * * 24 * * | 0 0 1 1 0 1 1 0 | 0 1 1 1 3 | 0 2 2
oo.o oo.o oo.o&#x & | 2 1 | 0 1 2 0 | * * * * 24 * | 0 0 0 0 1 2 1 0 | 0 0 3 1 2 | 0 1 3
...x ...x .... & | 0 4 | 0 0 0 4 | * * * * * 6 | 0 0 2 1 0 0 0 1 | 0 3 0 1 2 | 0 3 1
--------------------+-----+------------+-----------------+---------------------+-------------+------
xo.. ox.. ....&#x & ♦ 4 0 | 2 4 0 0 | 4 0 0 0 0 0 | 3 * * * * * * * | 2 0 0 2 0 | 1 1 2
xoo. .... ....&#x & ♦ 4 0 | 1 5 0 0 | 2 2 0 0 0 0 | * 12 * * * * * * | 2 0 1 0 0 | 1 0 2
x..x o..x ....&#x & ♦ 2 4 | 1 0 4 4 | 0 0 2 2 0 1 | * * 12 * * * * * | 0 1 0 1 1 | 0 2 1
.... o..x o..x&#x & ♦ 1 4 | 0 0 4 4 | 0 0 0 4 0 1 | * * * 6 * * * * | 0 1 0 0 2 | 0 2 1
oooo oooo oooo&#x ♦ 3 1 | 0 3 3 0 | 0 1 0 0 3 0 | * * * * 8 * * * | 0 0 3 0 0 | 0 0 3
xo.x .... ....&#x & ♦ 3 2 | 1 2 4 1 | 1 0 1 1 2 0 | * * * * * 24 * * | 0 0 1 1 1 | 0 1 2
.... .... oo.x&#x & ♦ 2 2 | 0 1 4 1 | 0 0 0 2 2 0 | * * * * * * 12 * | 0 0 1 0 2 | 0 1 2
...x ...x ...x ♦ 0 8 | 0 0 0 12 | 0 0 0 0 0 6 | * * * * * * * 1 | 0 3 0 0 0 | 0 3 0
--------------------+-----+------------+-----------------+---------------------+-------------+------
xoo. oxo. ....&#x & ♦ 5 0 | 2 8 0 0 | 6 4 0 0 0 0 | 1 4 0 0 0 0 0 0 | 6 * * * * | 1 0 1
x..x o..x o..x&#x & ♦ 2 8 | 1 0 8 12 | 0 0 4 8 0 6 | 0 0 4 2 0 0 0 1 | * 3 * * * | 0 2 0
xoox .... ....&#x & ♦ 4 2 | 1 5 6 1 | 2 2 1 2 6 0 | 0 1 0 0 2 2 1 0 | * * 12 * * | 0 0 2
xo.x ox.x ....&#x & ♦ 4 4 | 2 4 8 4 | 4 0 4 4 4 1 | 1 0 2 0 0 4 0 0 | * * * 6 * | 0 1 1
xo.x .... oo.x&#x & ♦ 3 4 | 1 2 8 4 | 1 0 2 6 4 1 | 0 0 1 1 0 2 2 0 | * * * * 12 | 0 1 1
--------------------+-----+------------+-----------------+---------------------+-------------+------
xoo. oxo. oox.&#x ♦ 6 0 | 3 12 0 0 | 12 8 0 0 0 0 | 3 12 0 0 0 0 0 0 | 6 0 0 0 0 | 1 * *
xo.x ox.x oo.x&#x & ♦ 4 8 | 2 4 16 12 | 4 0 8 16 8 6 | 1 0 8 4 0 8 4 1 | 0 2 0 2 4 | * 3 *
xoox oxox ....&#x & ♦ 5 4 | 2 8 12 4 | 6 4 4 8 12 1 | 1 4 2 1 4 8 4 0 | 1 0 4 1 2 | * * 6
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