Acronym	auteddi, J64
Name	augmented tridiminished icosahedron
	© ©
Vertex figures	[33], [3,52], [32,52], [33,5]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {5} (at join):   arccos(-sqrt[(5-2 sqrt(5))/15]) + arccos(1/3) = 171.341096° between {3} and {3} (of teddi):   arccos(-sqrt(5)/3) = 138.189685° between {3} and {5} (of teddi):   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317° between {3} and {3} (of tet):   arccos(1/3) = 70.528779° between {5} and {5}:   arccos(1/sqrt(5)) = 63.434949°
Face vector	10, 18, 10
Confer	uniform relatives: tet   ike   gad   related Johnson solids: teddi   general polytopal classes: Johnson solids
External links

Incidence matrix according to Dynkin symbol

oxfo3ooox&#xt   → height(1,2) = sqrt(2/3) = 0.816497
                  height(2,3) = sqrt[(3+sqrt(5))/6] = 0.934172
                  height(3,4) = 1/sqrt(3) = 0.577350
(pt || pseudo {3} || pseudo f-{3} || dual {3})

o...3o...     | 1 * * * | 3 0 0 0 0 | 3 0 0 0  tip, [33]
.o..3.o..     | * 3 * * | 1 2 1 0 0 | 2 2 0 0  [32,52]
..o.3..o.     | * * 3 * | 0 0 1 2 0 | 0 2 1 0  [3,52]
...o3...o     | * * * 3 | 0 0 0 2 2 | 0 1 2 1  [33,5]
--------------+---------+-----------+--------
oo..3oo..&#x  | 1 1 0 0 | 3 * * * * | 2 0 0 0
.x.. ....     | 0 2 0 0 | * 3 * * * | 1 1 0 0
.oo.3.oo.&#x  | 0 1 1 0 | * * 3 * * | 0 2 0 0  wedges
..oo3..oo&#x  | 0 0 1 1 | * * * 6 * | 0 1 1 0
.... ...x     | 0 0 0 2 | * * * * 3 | 0 0 1 1
--------------+---------+-----------+--------
ox.. ....&#x  | 1 2 0 0 | 2 1 0 0 0 | 3 * * *
.xfo ....&#xt | 0 2 2 1 | 0 1 2 2 0 | * 3 * *  
.... ..ox&#x  | 0 0 1 2 | 0 0 0 2 1 | * * 3 *
...o3...x     | 0 0 0 3 | 0 0 0 0 3 | * * * 1