Acronym mabidrid, J81
Name metabidiminished rhombicosidodecahedron
  
 © ©
Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figures [4,5,10], [3,4,5,4]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
  • between {4} and {10}:   arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474°
  • between {5} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Face vector 50, 90, 42
Confer
uniform relative:
srid  
related Johnson solids:
pecu   mabgyrid  
general polytopal classes:
Johnson solids  
External
links 		wikipedia   polytopewiki   mathworld   quickfur  

This polyhedron is an edge-faceting of the small rhombicosidodecahedron (srid).


Incidence matrix

4 * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0  [4,5,10] top
* 4 * * * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0  [4,5,10]
* * 2 * * * * * * * * * * * | 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0
* * * 4 * * * * * * * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0  [4,5,10]
* * * * 4 * * * * * * * * * | 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0
* * * * * 4 * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0  [4,5,10]
* * * * * * 4 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0  [4,5,10]
* * * * * * * 4 * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0
* * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 | 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0
* * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0
* * * * * * * * * * 2 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 | 0 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0
* * * * * * * * * * * 2 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 | 0 0 0 0 0 0 0 0 0 1 2 0 0 0 1 0
* * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0
* * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1  bottom
----------------------------+-----------------------------------------------------+--------------------------------
2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0  4-10
2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0  4-5
1 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0  5-10
0 1 1 0 0 0 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0  4-5
0 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * 4 * * * * * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0  4-10
0 0 1 0 1 0 0 0 0 0 0 0 0 0 | * * * * * 4 * * * * * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0  3-4
0 0 0 1 1 0 0 0 0 0 0 0 0 0 | * * * * * * 4 * * * * * * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0  4-5
0 0 0 1 0 1 0 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0  5-10
0 0 0 0 2 0 0 0 0 0 0 0 0 0 | * * * * * * * * 2 * * * * * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0  3-4
0 0 0 0 1 0 0 1 0 0 0 0 0 0 | * * * * * * * * * 4 * * * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0  4-5
0 0 0 0 0 1 1 0 0 0 0 0 0 0 | * * * * * * * * * * 4 * * * * * * * * * * * * * * * | 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0  4-10
0 0 0 0 0 1 0 0 1 0 0 0 0 0 | * * * * * * * * * * * 4 * * * * * * * * * * * * * * | 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0  4-5
0 0 0 0 0 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * 2 * * * * * * * * * * * * * | 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0  5-10
0 0 0 0 0 0 1 0 0 1 0 0 0 0 | * * * * * * * * * * * * * 4 * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0  4-5
0 0 0 0 0 0 0 2 0 0 0 0 0 0 | * * * * * * * * * * * * * * 2 * * * * * * * * * * * | 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0  3-4
0 0 0 0 0 0 0 1 1 0 0 0 0 0 | * * * * * * * * * * * * * * * 4 * * * * * * * * * * | 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0  4-5
0 0 0 0 0 0 0 1 0 0 0 1 0 0 | * * * * * * * * * * * * * * * * 4 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0  3-4
0 0 0 0 0 0 0 0 1 1 0 0 0 0 | * * * * * * * * * * * * * * * * * 4 * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0  3-4
0 0 0 0 0 0 0 0 1 0 0 0 1 0 | * * * * * * * * * * * * * * * * * * 4 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0  3-4
0 0 0 0 0 0 0 0 0 1 1 0 0 0 | * * * * * * * * * * * * * * * * * * * 4 * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0  4-5
0 0 0 0 0 0 0 0 0 1 0 0 1 0 | * * * * * * * * * * * * * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0  3-4
0 0 0 0 0 0 0 0 0 0 1 0 0 1 | * * * * * * * * * * * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0  3-4
0 0 0 0 0 0 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0  4-5
0 0 0 0 0 0 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0  4-5
0 0 0 0 0 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1  4-5
0 0 0 0 0 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1  3-4
----------------------------+-----------------------------------------------------+--------------------------------
4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * *  {4} top
2 2 1 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * *  {5}
2 2 0 2 0 2 2 0 0 0 0 0 0 0 | 1 0 2 0 2 0 0 2 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * *  {10}
0 1 1 1 1 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * *  {4}
0 0 1 0 2 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 2 * * * * * * * * * * *  {3}
0 0 0 1 1 1 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * 4 * * * * * * * * * *  {5}
0 0 0 0 2 0 0 2 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 2 * * * * * * * * *  {4} perp
0 0 0 0 0 1 1 0 1 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * *  {4}
0 0 0 0 0 0 2 0 0 2 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 2 0 0 0 0 0 0 | * * * * * * * * 2 * * * * * * *  {5}
0 0 0 0 0 0 0 2 0 0 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 2 * * * * * *  {3}
0 0 0 0 0 0 0 1 1 0 0 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 | * * * * * * * * * * 4 * * * * *  {4}
0 0 0 0 0 0 0 0 1 1 0 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 | * * * * * * * * * * * 4 * * * *  {3}
0 0 0 0 0 0 0 0 0 1 1 0 1 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 | * * * * * * * * * * * * 4 * * *  {4}
0 0 0 0 0 0 0 0 0 0 1 0 0 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 | * * * * * * * * * * * * * 2 * *  {3}
0 0 0 0 0 0 0 0 0 0 0 1 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 | * * * * * * * * * * * * * * 2 *  {5}
0 0 0 0 0 0 0 0 0 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * 1  {4} bottom

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