Acronym	toif
Name	toroidal icosahedron faceting, edge faceting ike-6-6-a
Circumradius	sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figure	[3,5,3,5/4,5/4]/0, [3,5,5]
Face vector	12, 24, 12
Confer	faceting of: ike
External links

This polyhedron is a toroidal edge-faceting of the icosidodecahedron (ike).

As an abstract polytope it happens to be selfdual.

Incidence matrix

3 * * * | 2 2 1 0 0 0 | 2 2 1 0  [3,5,3,5/4,5/4]/0
* 3 * * | 0 2 0 1 0 0 | 1 0 2 0  [3,5,5]
* * 3 * | 0 0 1 0 2 0 | 0 2 0 1  [3,5,5]
* * * 3 | 0 0 0 1 2 2 | 0 1 2 2  [3,5,3,5/4,5/4]/0
--------+-------------+--------
2 0 0 0 | 3 * * * * * | 1 1 0 0  top pseudo {3}
1 1 0 0 | * 6 * * * * | 1 0 1 0
1 0 1 0 | * * 3 * * * | 0 2 0 0
0 1 0 1 | * * * 3 * * | 0 0 2 0
0 0 1 1 | * * * * 6 * | 0 1 0 1
0 0 0 2 | * * * * * 3 | 0 0 1 1  bottom pseudo {3}
--------+-------------+--------
2 1 0 0 | 1 2 0 0 0 0 | 3 * * *  {3}
2 0 2 1 | 1 0 2 0 2 0 | * 3 * *  {5}
1 2 0 2 | 0 2 0 2 0 1 | * * 3 *  {5}
0 0 1 2 | 0 0 0 0 2 1 | * * * 3  {3}

or
6 *  & | 2  2 1 | 2 3  [3,5,3,5/4,5/4]/0
* 6  & | 0  2 1 | 1 2  [3,5,5]
-------+--------+----
2 0  & | 6  * * | 1 1  pseudo {3}
1 1  & | * 12 * | 1 1
1 1  & | *  * 6 | 0 2
-------+--------+----
2 1  & | 1  2 0 | 6 *  {3}
3 2  & | 1  2 2 | * 6  {5}