autpen

Acronym	autpen
Name	augmented truncated pentachoron
Circumradius	...
Lace city in approx. ASCII-art	x3o o3x -- oct x3o u3o x3x -- tut o3o u3o -- u-tet o3o x3o -- tet
Dihedral angles	at {3} between tet and trip: arccos(-sqrt[27/32]) = 156.716268° at {6} between tricu and tut: arccos(-7/8) = 151.044976° at {3} between oct and trip: arccos[-sqrt(3/8)] = 127.761244° at {4} between tricu and trip: arccos[-1/sqrt(6)] = 114.094843° at {3} between oct and tricu: arccos(-1/4) = 104.477512° at {3} between tet and tut: arccos(-1/4) = 104.477512° at {3} between tricu and tricu: arccos(1/4) = 75.522488° at {6} between tut and tut: arccos(1/4) = 75.522488°
Face vector	26, 64, 56, 18
Confer	uniform relative: tip segmentochora: octatut blend-components: octatut tip related CRFs: gyprip non-convex relatives: pautpen

The Stott expansion of this polychoron is gyprip.

Incidence matrix according to Dynkin symbol

oxux3xxoo3oooo&#xt   → all heights = sqrt(5/8) = 0.790569
(oct || pseudo tut || pseudo u-tet || tet)

o...3o...3o...     | 6  * * * |  4  2 0  0  0 0 0 | 2 2 1  4 0 0 0  0 0 | 1 2 2 0 0 0
.o..3.o..3.o..     | * 12 * * |  0  1 1  2  1 0 0 | 0 0 1  2 2 1 1  2 0 | 0 2 1 2 1 0
..o.3..o.3..o.     | *  * 4 * |  0  0 0  0  3 1 0 | 0 0 0  0 0 0 3  3 0 | 0 0 0 3 1 0
...o3...o3...o     | *  * * 4 |  0  0 0  0  0 1 3 | 0 0 0  0 0 0 3  0 3 | 0 0 0 3 0 1
-------------------+----------+-------------------+---------------------+------------
.... x... ....     | 2  0 0 0 | 12  * *  *  * * * | 1 1 0  1 0 0 0  0 0 | 1 1 1 0 0 0
oo..3oo..3oo..&#x  | 1  1 0 0 |  * 12 *  *  * * * | 0 0 1  2 0 0 0  0 0 | 0 2 1 0 0 0
.x.. .... ....     | 0  2 0 0 |  *  * 6  *  * * * | 0 0 1  0 2 0 1  0 0 | 0 2 0 2 0 0
.... .x.. ....     | 0  2 0 0 |  *  * * 12  * * * | 0 0 0  1 1 1 0  1 0 | 0 1 1 1 1 0
.oo.3.oo.3.oo.&#x  | 0  1 1 0 |  *  * *  * 12 * * | 0 0 0  0 0 0 1  2 0 | 0 0 0 2 1 0
..oo3..oo3..oo&#x  | 0  0 1 1 |  *  * *  *  * 4 * | 0 0 0  0 0 0 3  0 0 | 0 0 0 3 0 0
...x .... ....     | 0  0 0 2 |  *  * *  *  * * 6 | 0 0 0  0 0 0 1  0 2 | 0 0 0 2 0 1
-------------------+----------+-------------------+---------------------+------------
o...3x... ....     | 3  0 0 0 |  3  0 0  0  0 0 0 | 4 * *  * * * *  * * | 1 1 0 0 0 0
.... x...3o...     | 3  0 0 0 |  3  0 0  0  0 0 0 | * 4 *  * * * *  * * | 1 0 1 0 0 0
ox.. .... ....&#x  | 1  2 0 0 |  0  2 1  0  0 0 0 | * * 6  * * * *  * * | 0 2 0 0 0 0 (*)
.... xx.. ....&#x  | 2  2 0 0 |  1  2 0  1  0 0 0 | * * * 12 * * *  * * | 0 1 1 0 0 0
.x..3.x.. ....     | 0  6 0 0 |  0  0 3  3  0 0 0 | * * *  * 4 * *  * * | 0 1 0 1 0 0
.... .x..3.o..     | 0  3 0 0 |  0  0 0  3  0 0 0 | * * *  * * 4 *  * * | 0 0 1 0 1 0
.xux .... ....&#xt | 0  2 2 2 |  0  0 1  0  2 2 1 | * * *  * * * 6  * * | 0 0 0 2 0 0 (*)
.... .xo. ....&#x  | 0  2 1 0 |  0  0 0  1  2 0 0 | * * *  * * * * 12 * | 0 0 0 1 1 0
...x3...o ....     | 0  0 0 3 |  0  0 0  0  0 0 3 | * * *  * * * *  * 4 | 0 0 0 1 0 1
-------------------+----------+-------------------+---------------------+------------
o...3x...3o...     ♦ 6  0 0 0 | 12  0 0  0  0 0 0 | 4 4 0  0 0 0 0  0 0 | 1 * * * * *
ox..3xx.. ....&#x  ♦ 3  6 0 0 |  3  6 3  3  0 0 0 | 1 0 3  3 1 0 0  0 0 | * 4 * * * *
.... xx..3oo..&#x  ♦ 3  3 0 0 |  3  3 0  3  0 0 0 | 0 1 0  3 0 1 0  0 0 | * * 4 * * *
.xux3.xoo ....&#xt ♦ 0  6 3 3 |  0  0 3  3  6 3 3 | 0 0 0  0 1 0 3  3 1 | * * * 4 * *
.... .xo.3.oo.&#x  ♦ 0  3 1 0 |  0  0 0  3  3 0 0 | 0 0 0  0 0 1 0  3 0 | * * * * 4 *
...x3...o3...o     ♦ 0  0 0 4 |  0  0 0  0  0 0 6 | 0 0 0  0 0 0 0  0 4 | * * * * * 1

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