Acronym gyprip Name gyrated prip Circumradius sqrt(13/5) = 1.612452 Lace cityin approx. ASCII-art ``` o3x x3x x3o -- x3o3x (co) o3x u3x u3o -- u3o3x ((u,x)-co) x3x u3x x3u x3x -- x3x3x (toe) x3x o3u o3x -- o3x3x (inv. tut) ``` Dihedral angles at {6} between hip and tricu:   arccos(-sqrt[27/32]) = 156.716268° at {6} between tricu and tut:   arccos(-7/8) = 151.044976° at {4} between hip and trip:   arccos(-2/3) = 131.810315° at {3} between co and trip:   arccos(-sqrt[3/8]) = 127.761244° at {6} between hip and tut:   arccos(-sqrt[3/8]) = 127.761244° at {3} between tricu and trip:   arccos(-sqrt[3/8]) = 127.761244° at {4} between co and hip:   arccos(-sqrt[1/6]) = 114.094843° at {4} between hip and tricu:   arccos(-sqrt[1/6]) = 114.094843° at {3} between co and tut:   arccos(-1/4) = 104.477512° at {3} between tricu and tut:   arccos(-1/4) = 104.477512° Confer uniform relative: prip   segmentochora: tut || toe   related CRFs: co || (u,c)-co || toe   autpen

This polychoron is obtained from prip by dissection along its pseudo toe layer and then re-glueing those parts with interchanged roles of the hexagons. This dissects also the there located coes into pairs of tricues. Obviously this operation does not change its overall orbiformity. This is a rare case of true 4D gyration!

The Stott contraction of this polychoron is autpen.

Incidence matrix according to Dynkin symbol

```xuxo3ooxx3xxxx&#xt   → all heights = sqrt(5/8) = 0.790569
(co || pseudo (u,x)-co || pseudo toe || inv. tut)

o...3o...3o...     | 12  *  *  * |  2  2  1  0  0  0  0  0  0  0 0 | 1 2 1  2  2 0  0  0 0 0 0  0  0  0 0 0 | 1 1 2 1 0 0 0 0 0
.o..3.o..3.o..     |  * 12  *  * |  0  0  1  2  2  0  0  0  0  0 0 | 0 0 0  2  2 1  1  2 0 0 0  0  0  0 0 0 | 0 1 2 1 1 0 0 0 0
..o.3..o.3..o.     |  *  * 24  * |  0  0  0  0  1  1  1  1  1  0 0 | 0 0 0  1  0 0  1  1 1 1 1  1  1  1 0 0 | 0 1 1 0 1 1 1 1 0
...o3...o3...o     |  *  *  * 12 |  0  0  0  0  0  0  0  0  2  2 1 | 0 0 0  0  0 0  0  0 0 0 0  1  2  2 1 2 | 0 0 0 0 0 1 1 2 1
-------------------+-------------+---------------------------------+----------------------------------------+------------------
x... .... ....     |  2  0  0  0 | 12  *  *  *  *  *  *  *  *  * * | 1 1 0  1  0 0  0  0 0 0 0  0  0  0 0 0 | 1 1 1 0 0 0 0 0 0
.... .... x...     |  2  0  0  0 |  * 12  *  *  *  *  *  *  *  * * | 0 1 1  0  1 0  0  0 0 0 0  0  0  0 0 0 | 1 0 1 1 0 0 0 0 0
oo..3oo..3oo..&#x  |  1  1  0  0 |  *  * 12  *  *  *  *  *  *  * * | 0 0 0  2  2 0  0  0 0 0 0  0  0  0 0 0 | 0 1 2 1 0 0 0 0 0
.... .... .x..     |  0  2  0  0 |  *  *  * 12  *  *  *  *  *  * * | 0 0 0  0  1 1  0  1 0 0 0  0  0  0 0 0 | 0 0 1 1 1 0 0 0 0
.oo.3.oo.3.oo.&#x  |  0  1  1  0 |  *  *  *  * 24  *  *  *  *  * * | 0 0 0  1  0 0  1  1 0 0 0  0  0  0 0 0 | 0 1 1 0 1 0 0 0 0
..x. .... ....     |  0  0  2  0 |  *  *  *  *  * 12  *  *  *  * * | 0 0 0  1  0 0  0  0 1 1 0  1  0  0 0 0 | 0 1 1 0 0 1 1 0 0
.... ..x. ....     |  0  0  2  0 |  *  *  *  *  *  * 12  *  *  * * | 0 0 0  0  0 0  1  0 1 0 1  0  1  0 0 0 | 0 1 0 0 1 1 0 1 0
.... .... ..x.     |  0  0  2  0 |  *  *  *  *  *  *  * 12  *  * * | 0 0 0  0  0 0  0  1 0 1 1  0  0  1 0 0 | 0 0 1 0 1 0 1 1 0
..oo3..oo3..oo&#x  |  0  0  1  1 |  *  *  *  *  *  *  *  * 24  * * | 0 0 0  0  0 0  0  0 0 0 0  1  1  1 0 0 | 0 0 0 0 0 1 1 1 0
.... ...x ....     |  0  0  0  2 |  *  *  *  *  *  *  *  *  * 12 * | 0 0 0  0  0 0  0  0 0 0 0  0  1  0 1 1 | 0 0 0 0 0 1 0 1 1
.... .... ...x     |  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 6 | 0 0 0  0  0 0  0  0 0 0 0  0  0  2 0 2 | 0 0 0 0 0 0 1 2 1
-------------------+-------------+---------------------------------+----------------------------------------+------------------
x...3o... ....     |  3  0  0  0 |  3  0  0  0  0  0  0  0  0  0 0 | 4 * *  *  * *  *  * * * *  *  *  * * * | 1 1 0 0 0 0 0 0 0
x... .... x...     |  4  0  0  0 |  2  2  0  0  0  0  0  0  0  0 0 | * 6 *  *  * *  *  * * * *  *  *  * * * | 1 0 1 0 0 0 0 0 0
.... o...3x...     |  3  0  0  0 |  0  3  0  0  0  0  0  0  0  0 0 | * * 4  *  * *  *  * * * *  *  *  * * * | 1 0 0 1 0 0 0 0 0
xux. .... ....&#xt |  2  2  2  0 |  1  0  2  0  2  1  0  0  0  0 0 | * * * 12  * *  *  * * * *  *  *  * * * | 0 1 1 0 0 0 0 0 0
.... .... xx..&#x  |  2  2  0  0 |  0  1  2  1  0  0  0  0  0  0 0 | * * *  * 12 *  *  * * * *  *  *  * * * | 0 0 1 1 0 0 0 0 0
.... .o..3.x..     |  0  3  0  0 |  0  0  0  3  0  0  0  0  0  0 0 | * * *  *  * 4  *  * * * *  *  *  * * * | 0 0 0 1 1 0 0 0 0
.... .ox. ....&#x  |  0  1  2  0 |  0  0  0  0  2  0  1  0  0  0 0 | * * *  *  * * 12  * * * *  *  *  * * * | 0 1 0 0 1 0 0 0 0
.... .... .xx.&#x  |  0  2  2  0 |  0  0  0  1  2  0  0  1  0  0 0 | * * *  *  * *  * 12 * * *  *  *  * * * | 0 0 1 0 1 0 0 0 0
..x.3..x. ....     |  0  0  6  0 |  0  0  0  0  0  3  3  0  0  0 0 | * * *  *  * *  *  * 4 * *  *  *  * * * | 0 1 0 0 0 1 0 0 0
..x. .... ..x.     |  0  0  4  0 |  0  0  0  0  0  2  0  2  0  0 0 | * * *  *  * *  *  * * 6 *  *  *  * * * | 0 0 1 0 0 0 1 0 0
.... ..x.3..x.     |  0  0  6  0 |  0  0  0  0  0  0  3  3  0  0 0 | * * *  *  * *  *  * * * 4  *  *  * * * | 0 0 0 0 1 0 0 1 0
..xo .... ....&#x  |  0  0  2  1 |  0  0  0  0  0  1  0  0  2  0 0 | * * *  *  * *  *  * * * * 12  *  * * * | 0 0 0 0 0 1 1 0 0
.... ..xx ....&#x  |  0  0  2  2 |  0  0  0  0  0  0  1  0  2  1 0 | * * *  *  * *  *  * * * *  * 12  * * * | 0 0 0 0 0 1 0 1 0
.... .... ..xx&#x  |  0  0  2  2 |  0  0  0  0  0  0  0  1  2  0 1 | * * *  *  * *  *  * * * *  *  * 12 * * | 0 0 0 0 0 0 1 1 0
...o3...x ....     |  0  0  0  3 |  0  0  0  0  0  0  0  0  0  3 0 | * * *  *  * *  *  * * * *  *  *  * 4 * | 0 0 0 0 0 1 0 0 1
.... ...x3...x     |  0  0  0  6 |  0  0  0  0  0  0  0  0  0  3 3 | * * *  *  * *  *  * * * *  *  *  * * 4 | 0 0 0 0 0 0 0 1 1
-------------------+-------------+---------------------------------+----------------------------------------+------------------
x...3o...3x...     ♦ 12  0  0  0 | 12 12  0  0  0  0  0  0  0  0 0 | 4 6 4  0  0 0  0  0 0 0 0  0  0  0 0 0 | 1 * * * * * * * *
xux.3oox. ....&#xt ♦  3  3  6  0 |  3  0  3  0  6  3  3  0  0  0 0 | 1 0 0  3  0 0  3  0 1 0 0  0  0  0 0 0 | * 4 * * * * * * *
xux. .... xxx.&#xt ♦  4  4  4  0 |  2  2  4  2  4  2  0  2  0  0 0 | 0 1 0  2  2 0  0  2 0 1 0  0  0  0 0 0 | * * 6 * * * * * *
.... oo..3xx..&#x  ♦  3  3  0  0 |  0  3  3  3  0  0  0  0  0  0 0 | 0 0 1  0  3 1  0  0 0 0 0  0  0  0 0 0 | * * * 4 * * * * *
.... .ox.3.xx.&#x  ♦  0  3  6  0 |  0  0  0  3  6  0  3  3  0  0 0 | 0 0 0  0  0 1  3  3 0 0 1  0  0  0 0 0 | * * * * 4 * * * *
..xo3..xx ....&#x  ♦  0  0  6  3 |  0  0  0  0  0  3  3  0  6  3 0 | 0 0 0  0  0 0  0  0 1 0 0  3  3  0 1 0 | * * * * * 4 * * *
..xo .... ..xx&#x  ♦  0  0  4  2 |  0  0  0  0  0  2  0  2  4  0 1 | 0 0 0  0  0 0  0  0 0 1 0  2  0  2 0 0 | * * * * * * 6 * *
.... ..xx3..xx&#x  ♦  0  0  6  6 |  0  0  0  0  0  0  3  3  6  3 3 | 0 0 0  0  0 0  0  0 0 0 1  0  3  3 0 1 | * * * * * * * 4 *
...o3...x3...x     ♦  0  0  0 12 |  0  0  0  0  0  0  0  0  0 12 6 | 0 0 0  0  0 0  0  0 0 0 0  0  0  0 4 4 | * * * * * * * * 1
```