Acronym	tautid, J71
Name	triaugmented 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	75, 135, 62
Confer	uniform relative: tid   related Johnson solids: pecu   autid   mabautid   general polytopal classes: Johnson solids
External links

Incidence matrix

3 * * * * * * * * * * * * * * | 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0  [3,102] top
* 3 * * * * * * * * * * * * * | 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0  [3,102]
* * 6 * * * * * * * * * * * * | 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0  [3,4,3,10]
* * * 6 * * * * * * * * * * * | 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0  [3,4,3,10]
* * * * 6 * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0  [3,4,5,4]
* * * * * 6 * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0  [3,102]
* * * * * * 6 * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0  [3,4,3,10]
* * * * * * * 6 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0  [3,4,5,4]
* * * * * * * * 3 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 2 1 0 0 0 0  [3,4,5,4]
* * * * * * * * * 6 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0  [3,4,3,10]
* * * * * * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0  [3,4,3,10]
* * * * * * * * * * * 6 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0  [3,102]
* * * * * * * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 | 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0  [3,102]
* * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0  [3,102]
* * * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1  [3,102]
------------------------------+-------------------------------------------------------+--------------------------------
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{10} top
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * * * * * * * * * * * * | 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {10}-{10}
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{10}
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{4}
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0  {3}-{10}
0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * 6 * * * * * * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0  {3}-{4}
0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * 6 * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0  {3}-{4}
0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * 6 * * * * * * * * * * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0  {3}-{10}
0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * 6 * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0  {3}-{4}
0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 3 * * * * * * * * * * * * * * * * * | 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0  {4}-{5}
0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 | * * * * * * * * * * 6 * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0  {4}-{5}
0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 3 * * * * * * * * * * * * * * * | 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0  {10}-{10}
0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * 6 * * * * * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0  {3}-{10}
0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 | * * * * * * * * * * * * * 6 * * * * * * * * * * * * * | 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0  {3}-{4}
0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 | * * * * * * * * * * * * * * 6 * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0  {3}-{10}
0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 6 * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0  {4}-{5}
0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 | * * * * * * * * * * * * * * * * 6 * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0  {3}-{4}
0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 | * * * * * * * * * * * * * * * * * 6 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0  {3}-{4}
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 | * * * * * * * * * * * * * * * * * * 6 * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0  {3}-{4}
0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 | * * * * * * * * * * * * * * * * * * * 6 * * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * 3 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 | * * * * * * * * * * * * * * * * * * * * * 6 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | * * * * * * * * * * * * * * * * * * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0  {10}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 | * * * * * * * * * * * * * * * * * * * * * * * 3 * * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * * * * * * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0  {10}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1  {3}-{10} bottom
------------------------------+-------------------------------------------------------+--------------------------------
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * *  {3} top
2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 | 1 2 2 0 2 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * *  {10} upper
0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * *  {3}
0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * * * * * *  {4}
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * *  {3}
0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 6 * * * * * * * * * *  {3}
0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 6 * * * * * * * * *  {4}
0 0 0 0 2 0 0 2 1 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * 3 * * * * * * * *  {5}
0 0 0 0 0 2 2 0 0 2 0 2 2 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2 0 0 0 0 2 0 0 2 1 0 0 0 | * * * * * * * * 3 * * * * * * *  {10} medial
0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 6 * * * * * *  {3}
0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * 6 * * * * *  {4}
0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 | * * * * * * * * * * * 3 * * * *  {3}
0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 | * * * * * * * * * * * * 6 * * *  {3}
0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 2 2 1 | * * * * * * * * * * * * * 3 * *  {10} lower
0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 | * * * * * * * * * * * * * * 3 *  {3}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * 1  {3} bottom