octum

Acronym	octum
Name	octahedron-first rotunda of truncated hexadecachoron, oct-based tutsatope, oct-based tutism
	©
Circumradius	sqrt(5/2) = 1.581139
Lace city in approx. ASCII-art	o4o x4o o4o o4o u4o o4o x4o u4o x4q u4o x4o
Lace city in approx. ASCII-art	x3x u3o x3o u3x o3x x3u o3u x3x
Coordinates	(sqrt(2), 1/sqrt(2), 0, 0) & all permutations; all changes of sign but in last coordinate
Dihedral angles	at {3} between oct and tut: 120° at {3} between squippy and tut: 120° at {6} between tut and tut: 120° at {4} between squippy and toe: 90° at {6} between toe and tut: 60°
Face vector	36, 78, 58, 16
Confer	uniform relative: thex related CRFs: oxux3xxoo4oooo&#xt general polytopal classes: tutsatopes bistratic lace towers

Incidence matrix according to Dynkin symbol

xux3oox4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(oct || pseudo u-oct || toe)

o..3o..4o..     | 6 *  * |  4 1  0  0  0 | 4  4  0 0 0 | 1 4 0 0
.o.3.o.4.o.     | * 6  * |  0 1  4  0  0 | 0  4  4 0 0 | 0 4 1 0
..o3..o4..o     | * * 24 |  0 0  1  1  2 | 0  1  2 2 1 | 0 2 1 1
----------------+--------+---------------+-------------+--------
x.. ... ...     | 2 0  0 | 12 *  *  *  * | 2  1  0 0 0 | 1 2 0 0
oo.3oo.4oo.&#x  | 1 1  0 |  * 6  *  *  * | 0  4  0 0 0 | 0 4 0 0
.oo3.oo4.oo&#x  | 0 1  1 |  * * 24  *  * | 0  1  2 0 0 | 0 2 1 0
..x ... ...     | 0 0  2 |  * *  * 12  * | 0  1  0 2 0 | 0 2 0 1
... ..x ...     | 0 0  2 |  * *  *  * 24 | 0  0  1 1 1 | 0 1 1 1
----------------+--------+---------------+-------------+--------
x..3o.. ...     | 3 0  0 |  3 0  0  0  0 | 8  *  * * * | 1 1 0 0
xux ... ...&#xt | 2 2  2 |  1 2  2  1  0 | * 12  * * * | 0 2 0 0
... .ox ...&#x  | 0 1  2 |  0 0  2  0  1 | *  * 24 * * | 0 1 1 0
..x3..x ...     | 0 0  6 |  0 0  0  3  3 | *  *  * 8 * | 0 1 0 1
... ..x4..o     | 0 0  4 |  0 0  0  0  4 | *  *  * * 6 | 0 0 1 1
----------------+--------+---------------+-------------+--------
x..3o..4o..     ♦ 6 0  0 | 12 0  0  0  0 | 8  0  0 0 0 | 1 * * *
xux3oox ...&#xt ♦ 3 3  6 |  3 3  6  3  3 | 1  3  3 1 0 | * 8 * *
... .ox4.oo&#x  ♦ 0 1  4 |  0 0  4  0  4 | 0  0  4 0 1 | * * 6 *
..x3..x4..o     ♦ 0 0 24 |  0 0  0 12 24 | 0  0  0 8 6 | * * * 1

oox3xux3oox&#xt   → all heights = 1/sqrt(2) = 0.707107
(oct || pseudo u-oct || toe)

o....3o....3o....     | 6 *  * |  4 1  0  0  0  0 | 2 2  4  0  0 0 0 0 | 1 2 2 0 0
.o...3.o...3.o...     | * 6  * |  0 1  4  0  0  0 | 0 0  4  2  2 0 0 0 | 0 2 2 1 0
..o..3..o..3..o..     | * * 24 |  0 0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
----------------------+--------+------------------+--------------------+----------
..... x.... .....     | 2 0  0 | 12 *  *  *  *  * | 1 1  1  0  0 0 0 0 | 1 1 1 0 0
oo...3oo...3oo...&#x  | 1 1  0 |  * 6  *  *  *  * | 0 0  4  0  0 0 0 0 | 0 2 2 0 0
.oo..3.oo..3.oo..&#x  | 0 1  1 |  * * 24  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
..x.. ..... .....     | 0 0  2 |  * *  * 12  *  * | 0 0  0  1  0 1 1 0 | 0 1 0 1 1
..... ..x.. .....     | 0 0  2 |  * *  *  * 12  * | 0 0  1  0  0 1 0 1 | 0 1 1 0 1
..... ..... ..x..     | 0 0  2 |  * *  *  *  * 12 | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
----------------------+--------+------------------+--------------------+----------
o....3x.... .....     | 3 0  0 |  3 0  0  0  0  0 | 4 *  *  *  * * * * | 1 1 0 0 0
..... x....3o....     | 3 0  0 |  3 0  0  0  0  0 | * 4  *  *  * * * * | 1 0 1 0 0
..... xux.. .....&#xt | 2 2  2 |  1 2  2  0  1  0 | * * 12  *  * * * * | 0 1 1 0 0
.ox.. ..... .....&#x  | 0 1  2 |  0 0  2  1  0  0 | * *  * 12  * * * * | 0 1 0 1 0
..... ..... .ox..&#x  | 0 1  2 |  0 0  2  0  0  1 | * *  *  * 12 * * * | 0 0 1 1 0
..x..3..x.. .....     | 0 0  6 |  0 0  0  3  3  0 | * *  *  *  * 4 * * | 0 1 0 0 1
..x.. ..... ..x..     | 0 0  4 |  0 0  0  2  0  2 | * *  *  *  * * 6 * | 0 0 0 1 1
..... ..x..3..x..     | 0 0  6 |  0 0  0  0  3  3 | * *  *  *  * * * 4 | 0 0 1 0 1
----------------------+--------+------------------+--------------------+----------
o....3x....3o....     ♦ 6 0  0 | 12 0  0  0  0  0 | 4 4  0  0  0 0 0 0 | 1 * * * *
oox..3xux.. .....&#xt ♦ 3 3  6 |  3 3  6  3  3  0 | 1 0  3  3  0 1 0 0 | * 4 * * *
..... xux..3oox..&#xt ♦ 3 3  6 |  3 3  6  0  3  3 | 0 1  3  0  3 0 0 1 | * * 4 * *
.ox.. ..... .ox..&#xt ♦ 0 1  4 |  0 0  4  2  0  2 | 0 0  0  2  2 0 1 0 | * * * 6 *
..x..3..x..3..x..     ♦ 0 0 24 |  0 0  0 12 12 12 | 0 0  0  0  0 4 6 4 | * * * * 1

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