Acronym pabgyrid, J73
Name parabigyrated rhombicosidodecahedron
 
 © ©
Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figures [3,4,4,5], [3,4,5,4]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {3} and {5}:   arccos(-sqrt[(65-2 sqrt(5))/75]) = 153.942419°
  • between {4} and {4}:   arccos(-2/sqrt(5)) = 153.434949°
  • between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
Confer
uniform relative:
srid  
related Johnson solids:
pecu   pabidrid  
general polytopal classes:
Johnson solids  
External
links
wikipedia   mathworld

Incidence matrix

5  *  * * *  *  * * | 2  2 0 0  0 0  0  0  0  0 0  0 0 0  0 0 | 1 2 1 0 0 0  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 | 0 1 1 1 1 0  0 0 0 0 0 0 0  upper gyration level
*  * 10 * *  *  * * | 0  0 0 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 0
*  *  * 5 *  *  * * | 0  0 0 0  0 0  2  0  2  0 0  0 0 0  0 0 | 0 0 0 0 1 0  2 1 0 0 0 0 0
*  *  * * 5  *  * * | 0  0 0 0  0 0  0  2  0  2 0  0 0 0  0 0 | 0 0 0 0 0 1  2 0 1 0 0 0 0
*  *  * * * 10  * * | 0  0 0 0  0 0  0  0  1  1 1  1 0 0  0 0 | 0 0 0 0 0 0  1 1 1 1 0 0 0
*  *  * * *  * 10 * | 0  0 0 0  0 0  0  0  0  0 0  1 1 1  1 0 | 0 0 0 0 0 0  0 0 1 1 1 1 0  lower gyration level
*  *  * * *  *  * 5 | 0  0 0 0  0 0  0  0  0  0 0  0 0 0  2 2 | 0 0 0 0 0 0  0 0 0 0 1 2 1  bottom
--------------------+-----------------------------------------+---------------------------
2  0  0 0 0  0  0 0 | 5  * * *  * *  *  *  *  * *  * * *  * * | 1 1 0 0 0 0  0 0 0 0 0 0 0  top
1  1  0 0 0  0  0 0 | * 10 * *  * *  *  *  *  * *  * * *  * * | 0 1 1 0 0 0  0 0 0 0 0 0 0
0  2  0 0 0  0  0 0 | *  * 5 *  * *  *  *  *  * *  * * *  * * | 0 1 0 1 0 0  0 0 0 0 0 0 0  {4},{4}-edge
0  2  0 0 0  0  0 0 | *  * * 5  * *  *  *  *  * *  * * *  * * | 0 0 1 0 1 0  0 0 0 0 0 0 0  {5},{3}-edge
0  1  1 0 0  0  0 0 | *  * * * 10 *  *  *  *  * *  * * *  * * | 0 0 0 1 1 0  0 0 0 0 0 0 0
0  0  2 0 0  0  0 0 | *  * * *  * 5  *  *  *  * *  * * *  * * | 0 0 0 1 0 1  0 0 0 0 0 0 0
0  0  1 1 0  0  0 0 | *  * * *  * * 10  *  *  * *  * * *  * * | 0 0 0 0 1 0  1 0 0 0 0 0 0
0  0  1 0 1  0  0 0 | *  * * *  * *  * 10  *  * *  * * *  * * | 0 0 0 0 0 1  1 0 0 0 0 0 0
0  0  0 1 0  1  0 0 | *  * * *  * *  *  * 10  * *  * * *  * * | 0 0 0 0 0 0  1 1 0 0 0 0 0
0  0  0 0 1  1  0 0 | *  * * *  * *  *  *  * 10 *  * * *  * * | 0 0 0 0 0 0  1 0 1 0 0 0 0
0  0  0 0 0  2  0 0 | *  * * *  * *  *  *  *  * 5  * * *  * * | 0 0 0 0 0 0  0 1 0 1 0 0 0
0  0  0 0 0  1  1 0 | *  * * *  * *  *  *  *  * * 10 * *  * * | 0 0 0 0 0 0  0 0 1 1 0 0 0
0  0  0 0 0  0  2 0 | *  * * *  * *  *  *  *  * *  * 5 *  * * | 0 0 0 0 0 0  0 0 1 0 1 0 0  {5},{3}-edge
0  0  0 0 0  0  2 0 | *  * * *  * *  *  *  *  * *  * * 5  * * | 0 0 0 0 0 0  0 0 0 1 0 1 0  {4},{4}-edge
0  0  0 0 0  0  1 1 | *  * * *  * *  *  *  *  * *  * * * 10 * | 0 0 0 0 0 0  0 0 0 0 1 1 0
0  0  0 0 0  0  0 2 | *  * * *  * *  *  *  *  * *  * * *  * 5 | 0 0 0 0 0 0  0 0 0 0 0 1 1  bottom
--------------------+-----------------------------------------+---------------------------
5  0  0 0 0  0  0 0 | 5  0 0 0  0 0  0  0  0  0 0  0 0 0  0 0 | 1 * * * * *  * * * * * * *  top
2  2  0 0 0  0  0 0 | 1  2 1 0  0 0  0  0  0  0 0  0 0 0  0 0 | * 5 * * * *  * * * * * * *
1  2  0 0 0  0  0 0 | 0  2 0 1  0 0  0  0  0  0 0  0 0 0  0 0 | * * 5 * * *  * * * * * * *
0  2  2 0 0  0  0 0 | 0  0 1 0  2 1  0  0  0  0 0  0 0 0  0 0 | * * * 5 * *  * * * * * * *
0  2  2 1 0  0  0 0 | 0  0 0 1  2 0  2  0  0  0 0  0 0 0  0 0 | * * * * 5 *  * * * * * * *
0  0  2 0 1  0  0 0 | 0  0 0 0  0 1  0  2  0  0 0  0 0 0  0 0 | * * * * * 5  * * * * * * *
0  0  1 1 1  1  0 0 | 0  0 0 0  0 0  1  1  1  1 0  0 0 0  0 0 | * * * * * * 10 * * * * * *
0  0  0 1 0  2  0 0 | 0  0 0 0  0 0  0  0  2  0 1  0 0 0  0 0 | * * * * * *  * 5 * * * * *
0  0  0 0 1  2  2 0 | 0  0 0 0  0 0  0  0  0  2 0  2 1 0  0 0 | * * * * * *  * * 5 * * * *
0  0  0 0 0  2  2 0 | 0  0 0 0  0 0  0  0  0  0 1  2 0 1  0 0 | * * * * * *  * * * 5 * * *
0  0  0 0 0  0  2 1 | 0  0 0 0  0 0  0  0  0  0 0  0 1 0  2 0 | * * * * * *  * * * * 5 * *
0  0  0 0 0  0  2 2 | 0  0 0 0  0 0  0  0  0  0 0  0 0 1  2 1 | * * * * * *  * * * * * 5 *
0  0  0 0 0  0  0 5 | 0  0 0 0  0 0  0  0  0  0 0  0 0 0  0 5 | * * * * * *  * * * * * * 1  bottom
or
10  *  *  * |  2  2  0  0  0  0  0  0 | 1  2  1  0  0  0  0  polar
 * 20  *  * |  0  1  1  1  1  0  0  0 | 0  1  1  1  1  0  0  gyration level
 *  * 20  * |  0  0  0  0  1  1  1  1 | 0  0  0  1  1  1  1  tropical
 *  *  * 10 |  0  0  0  0  0  0  2  2 | 0  0  0  0  1  1  2  medial
------------+-------------------------+--------------------
 2  0  0  0 | 10  *  *  *  *  *  *  * | 1  1  0  0  0  0  0  polar
 1  1  0  0 |  * 20  *  *  *  *  *  * | 0  1  1  0  0  0  0
 0  2  0  0 |  *  * 10  *  *  *  *  * | 0  1  0  1  0  0  0  {4},{4}-edge
 0  2  0  0 |  *  *  * 10  *  *  *  * | 0  0  1  0  1  0  0  {5},{3}-edge
 0  1  1  0 |  *  *  *  * 20  *  *  * | 0  0  0  1  1  0  0
 0  0  2  0 |  *  *  *  *  * 10  *  * | 0  0  0  1  0  1  0
 0  0  1  1 |  *  *  *  *  *  * 20  * | 0  0  0  0  1  0  1  {4},{5}-join
 0  0  1  1 |  *  *  *  *  *  *  * 20 | 0  0  0  0  0  1  1  {3},{4}-join
------------+-------------------------+--------------------
 5  0  0  0 |  5  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *
 2  2  0  0 |  1  2  1  0  0  0  0  0 | * 10  *  *  *  *  *
 1  2  0  0 |  0  2  0  1  0  0  0  0 | *  * 10  *  *  *  *
 0  2  2  0 |  0  0  1  0  2  1  0  0 | *  *  * 10  *  *  *
 0  2  2  1 |  0  0  0  1  2  0  2  0 | *  *  *  * 10  *  *
 0  0  2  1 |  0  0  0  0  0  1  0  2 | *  *  *  *  * 10  *
 0  0  2  2 |  0  0  0  0  0  0  2  2 | *  *  *  *  *  * 10  equatorial {4}

© 2004-2018
top of page