Acronym	autid, J68
Name	augmented truncated dodecahedron
	© ©   ©
Vertex figure	[3,4,5,4], [3,4,3,10], [3,102]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {4} (at join):   arccos(-sqrt[(5+2 sqrt(5))/15]) + arccos(sqrt[(5+sqrt(5))/10]) = 174.340106° between {3} and {4} (pecu lacings):   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843° between {4} and {10}:   arccos(-sqrt[(65-2 sqrt(5))/75]) = 153.942419° between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526° between {3} and {10}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632° between {10} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Face vector	65, 105, 42
Confer	uniform relative: tid   related Johnson solids: pecu   pabautid   mabautid   tautid   general polytopal classes: Johnson solids
External links

Incidence matrix

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