Acronym mibkid
Name metabikis dodecahedron,
(subsymmetrically) metabistellated-dodecahedron,
dual of mibdi
Vertex figures [52,K], [5,K2], [T,K2], [t,k3]
Dual mibdi
Dihedral angles
  • at small edges v:   arccos(-1/sqrt(5)) = 116.565051°
  • at medium edges f:   arccos(-1/sqrt(5)) = 116.565051°
  • at long edges F:   arccos(-1/sqrt(5)) = 116.565051°
Confer
related Johnson solids:
mibdi  
uniform relative:
doe  

The faces are kites {(k,K,K,K)} with corner angle k = 36° and K = 108°, where side KK has size v = (sqrt(5)-1)/2 = 0.618034, diagonal KK has size x = 1, side kK has size f = (1+sqrt(5))/2 = 1.618034, and diagonal kK has size sqrt[(5+sqrt(5))/2] = 1.902113, golden triangles {(T,t,t)} with the same corner angles t = 36° and T = 108°, where side tT has the same size f, while side tt has size F = (3+sqrt(5))/2 = 2.618034, resp. regular, v-sized pentagons.


Incidence matrix

F2o || pseudo o2f || pseudo f2v || pseudo o2f || pseudo x2x || v2o
where: height(1,2) = 1/2
       height(2,3) = v = (sqrt(5)-1)/2 = 0.618034
       height(3,4) = (3-sqrt(5))/4 = 0.190983
       height(4,5) = (sqrt(5)-1)/4 = 0.309017

2 * * * * | 1 2 2 0 0 0 0 | 2 2 1 0  [t,k3]
* 2 * * * | 0 2 0 1 0 0 0 | 1 2 0 0  [T,K2]
* * 2 * * | 0 0 0 1 2 0 0 | 0 2 0 1  [5,K2]
* * * 4 * | 0 0 1 0 1 1 0 | 0 1 1 1  [5,K2]
* * * * 2 | 0 0 0 0 0 2 1 | 0 0 1 2  [52,K]
----------+---------------+--------
2 0 0 0 0 | 1 * * * * * * | 2 0 0 0  F
1 1 0 0 0 | * 4 * * * * * | 1 1 0 0  f
1 0 0 1 0 | * * 4 * * * * | 0 1 1 0  f
0 1 1 0 0 | * * * 2 * * * | 0 2 0 0  v
0 0 1 1 0 | * * * * 4 * * | 0 1 0 1  v
0 0 0 1 1 | * * * * * 4 * | 0 0 1 1  v
0 0 0 0 2 | * * * * * * 1 | 0 0 0 2  v
----------+---------------+--------
2 1 0 0 0 | 1 2 0 0 0 0 0 | 2 * * *  {(T,t,t)}
1 1 1 1 0 | 0 1 1 1 1 0 0 | * 4 * *  {(k,K,K,K)}
1 0 0 2 1 | 0 0 2 0 0 2 0 | * * 2 *  {(k,K,K,K)}
0 0 1 2 2 | 0 0 0 0 2 2 1 | * * * 2  {5}

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