Acronym	gyepip, J11
Name	gyroelongated pentagonal pyramid, diminished icosahedron
	© ©
Vertex figure	[35], [33,5]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – other member: digdom – other edge facetings)
Dihedral angles	between {3} and {3}:   arccos(-sqrt(5)/3) = 138.189685° between {3} and {5}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
Face vector	11, 25, 16
Confer	uniform relative: ike   pap   related Johnson solids: peppy   teddi   general polytopal classes: Johnson solids   bistratic lace towers
External links

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

Incidence matrix according to Dynkin symbol

oxo5oox&#xt   → height(1,2) = sqrt[(5-sqrt(5))/10] = 0.525731
                height(2,3) = sqrt[(5+sqrt(5))/10] = 0.850651
(pt || pseudo {5} || dual {5})

o..5o..    | 1 * * | 5 0  0 0 | 5 0 0 0
.o.5.o.    | * 5 * | 1 2  2 0 | 2 2 1 0
..o5..o    | * * 5 | 0 0  2 2 | 0 1 2 1
-----------+-------+----------+--------
oo.5oo.&#x | 1 1 0 | 5 *  * * | 2 0 0 0
.x. ...    | 0 2 0 | * 5  * * | 1 1 0 0
.oo5.oo&#x | 0 1 1 | * * 10 * | 0 1 1 0
... ..x    | 0 0 2 | * *  * 5 | 0 0 1 1
-----------+-------+----------+--------
ox. ...&#x | 1 2 0 | 2 1  0 0 | 5 * * *
.xo ...&#x | 0 2 1 | 0 1  2 0 | * 5 * *
... .ox&#x | 0 1 2 | 0 0  2 1 | * * 5 *
..x5..o    | 0 0 5 | 0 0  0 5 | * * * 1