Acronym	digdom, ike-5-7
Name	diminished ike-gad morpher, 5-fold pyramidal-symmetric ike faceting with 5 trigs and 7 pigs
Vertex figure	[55]/2, [5/423,5,3]/0, [3/2,53]
General of army	gyepip
Colonel of regiment	gyepip
Dihedral angles	between {3} and {5}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317° between {3} and {5}:   arccos(sqrt[(5-2 sqrt(5))/15]) = 79.187683° between {5} and {5}:   arccos(1/sqrt(5)) = 63.434949°
Face vector	11, 25, 12
Confer	uniform relative: ike   gad   related Johnson solids: gyepip
External links

This polyhedron is an edge-faceting of the icosahedron (ike).

Incidence matrix according to Dynkin symbol

o(-x)o5ofx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/10] = 0.525731
                   height(2,3) = sqrt[(5+sqrt(5))/10] = 0.850651
(pt || "complete {5}" || dual {5})

o  . .5o..     | 1 * * | 5 0  0 0 | 5 0 0 0  [55]/2
.  o .5.o.     | * 5 * | 1 2  2 0 | 2 1 2 0  [5/423,5,3]/0
.  . o5..o     | * * 5 | 0 0  2 2 | 2 0 1 1  [3/2,53]
---------------+-------+----------+--------
o  o .5oo.&#x  | 1 1 0 | 5 *  * * | 2 0 0 0
.(-x). ...     | 0 2 0 | * 5  * * | 0 1 1 0
.  o o5.oo&#x  | 0 1 1 | * * 10 * | 1 0 1 0
.  . . ..x     | 0 0 2 | * *  * 5 | 1 0 0 1
---------------+-------+----------+--------
.  . . ofx&#xt | 1 2 2 | 2 0  2 1 | 5 * * *  {5}
.(-x).5.o.     | 0 5 0 | 0 5  0 0 | * 1 * *  {5}
.(-x)o ...&#x  | 0 2 1 | 0 1  2 0 | * * 5 *  {3}
.  . o5..x     | 0 0 5 | 0 0  0 5 | * * * 1  {5}