Acronym ...
Name vertex figure of pental disnubbachoron,
biform twirled compound of 2 vertex-first icosahedra
 
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Circumradius sqrt[(5+sqrt(5))/8] = 0.951057

This compound occurs in 3 different forms depending on whether the axial vertices (coincident by 2) will be counted separately (type A), or will be identified (type B). – Further a representation is given as (type C), which is induced by the around symmetry when being used as vertex figure of pental disnubbachoron. There the color coding of the above picture gets refered.


Incidence matrix

(Type A) – no identifications of coincident elements

4  * |  5  0  0 |  5  0 || 1
* 20 |  1  2  2 |  2  3 || 1
-----+----------+-------++--
1  1 | 20  *  * |  2  0 || 1
0  2 |  * 20  * |  1  1 || 1  on tropal circle
0  2 |  *  * 20 |  0  2 || 1  equatorial zick-zacks
-----+----------+-------++--
1  2 |  2  1  0 | 20  * || 1
0  3 |  0  1  2 |  * 20 || 1
-----+----------+-------++--
2 10 | 10 10 10 | 10 10 || 2  ike

(Type B) – identifying vertices, no around symmetry implications

2  * | 10  0  0 | 10  0 || 2  axial
* 20 |  1  2  2 |  2  3 || 1  tropal
-----+----------+-------++--
1  1 | 20  *  * |  2  0 || 1
0  2 |  * 20  * |  1  1 || 1  on tropal circle
0  2 |  *  * 20 |  0  2 || 1  equatorial zick-zacks
-----+----------+-------++--
1  2 |  2  1  0 | 20  * || 1
0  3 |  0  1  2 |  * 20 || 1
-----+----------+-------++--
2 10 | 10 10 10 | 10 10 || 2  ike

(Type C) – identifying vertices, with pedisna induced around symmetry implications

2  *  * |  5  5  0 0 0  0 0 0 |  5  5  0  0 || 1 1  axial
* 10  * |  1  0  2 1 1  0 0 0 |  2  0  3  0 || 1 0  of red ike
*  * 10 |  0  1  0 0 0  2 1 1 |  0  2  0  3 || 0 1  of yellow ike
--------+---------------------+-------------++----
1  1  0 | 10  *  * * *  * * * |  2  0  0  0 || 1 0  green, of red ike (acc. to right sisp-verf)
1  0  1 |  * 10  * * *  * * * |  0  2  0  0 || 0 1  cyan, of yellow ike (acc. to left sisp-verf)
0  2  0 |  *  * 10 * *  * * * |  1  0  1  0 || 1 0  orange, on tropal circle of red ike (acc. to left spysp-verf)
0  2  0 |  *  *  * 5 *  * * * |  0  0  2  0 || 1 0  green, right equatorial zick-zack of red ike (acc. to right sisp-verf)
0  2  0 |  *  *  * * 5  * * * |  0  0  2  0 || 1 0  orange, left equatorial zick-zack of red ike (acc. to left spysp-verf)
0  0  2 |  *  *  * * * 10 * * |  0  1  0  1 || 0 1  magenta, on tropal circle of yellow ike (acc. to right spysp-verf)
0  0  2 |  *  *  * * *  * 5 * |  0  0  0  2 || 0 1  magenta, right equatorial zick-zack of yellow ike (acc. to right spysp-verf)
0  0  2 |  *  *  * * *  * * 5 |  0  0  0  2 || 0 1  cyan, left equatorial zick-zack of yellow ike (acc. to left sisp-verf)
--------+---------------------+-------------++----
1  2  0 |  2  0  1 0 0  0 0 0 | 10  *  *  * || 1 0  green-green-orange, of red ike
1  0  2 |  0  2  0 0 0  1 0 0 |  * 10  *  * || 0 1  cyan-cyan-magenta, of yellow ike
0  3  0 |  0  0  1 1 1  0 0 0 |  *  * 10  * || 1 0  green-orange-orange, of red ike
0  0  3 |  0  0  0 0 0  1 1 1 |  *  *  * 10 || 0 1  cyan-magenta-magenta, of yellow ike
--------+---------------------+-------------++----
2 10  0 | 10  0 10 5 5  0 0 0 | 10  0 10  0 || 1 *  red ike
2  0 10 |  0 10  0 0 0 10 5 5 |  0 10  0 10 || * 1  yellow ike

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