Acronym	gyepabro, J48
Name	gyroelongated pentagonal birotunda
	© ©
Vertex figure	[(3,5)2], [34,5]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	40, 90, 52
Confer	uniform relative: dap   related Johnson solids: pero   gyepro   general polytopal classes: Johnson solids
External links

A chiral polyhedron coming in 2 enantiomorph versions.

Incidence matrix

5 * * * * * * * | 2 1 1 0 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  top
* 5 * * * * * * | 0 1 1 1 1 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  upper medial
* * 5 * * * * * | 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 1 1 0 0 0 0 0  upp. tropal above {5}
* * * 5 * * * * | 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 | 0 0 1 1 1 1 0 1 0 0 0 0  upp. tropal above {3}
* * * * 5 * * * | 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 | 0 0 0 0 1 0 1 1 1 1 0 0  low. tropal undn. {5}
* * * * * 5 * * | 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 | 0 0 0 0 0 1 1 1 1 1 0 0  low. tropal undn. {3}
* * * * * * 5 * | 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 2 1 1 0  lower medial
* * * * * * * 5 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 | 0 0 0 0 0 0 0 0 1 0 2 1  bottom
----------------+-------------------------------------+------------------------
2 0 0 0 0 0 0 0 | 5 * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 0  top
1 1 0 0 0 0 0 0 | * 5 * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 | * * 5 * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 | * * * 5 * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 | * * * * 5 * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 | * * * * * 5 * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0 0  tropical {5},{3} joins
0 0 1 1 0 0 0 0 | * * * * * * 5 * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 0 0  tropical {3},{3} joins
0 0 1 0 1 0 0 0 | * * * * * * * 5 * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 0
0 0 1 0 0 1 0 0 | * * * * * * * * 5 * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 0 0 0 | * * * * * * * * * 5 * * * * * * * * | 0 0 0 0 1 0 0 1 0 0 0 0
0 0 0 1 0 1 0 0 | * * * * * * * * * * 5 * * * * * * * | 0 0 0 0 0 1 0 1 0 0 0 0
0 0 0 0 1 1 0 0 | * * * * * * * * * * * 5 * * * * * * | 0 0 0 0 0 0 1 0 1 0 0 0  tropical {3},{5} joins
0 0 0 0 1 1 0 0 | * * * * * * * * * * * * 5 * * * * * | 0 0 0 0 0 0 0 1 0 1 0 0  tropical {3},{3} joins
0 0 0 0 1 0 1 0 | * * * * * * * * * * * * * 5 * * * * | 0 0 0 0 0 0 0 0 1 1 0 0
0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * 5 * * * | 0 0 0 0 0 0 0 0 1 1 0 0
0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * 5 * * | 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * 5 * | 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * 5 | 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 0 0 | 1 * * * * * * * * * * *  top {5}
2 1 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 5 * * * * * * * * * *
1 2 1 1 0 0 0 0 | 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * 5 * * * * * * * * *  upper {5}
0 1 1 1 0 0 0 0 | 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * 5 * * * * * * * *
0 0 1 1 1 0 0 0 | 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 | * * * * 5 * * * * * * *  equ. {3} undn. {5}
0 0 1 1 0 1 0 0 | 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 | * * * * * 5 * * * * * *  equ. {3} undn. {3}
0 0 1 0 1 1 0 0 | 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 | * * * * * * 5 * * * * *  equ. {3} above {5}
0 0 0 1 1 1 0 0 | 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 | * * * * * * * 5 * * * *  equ. {3} above {3}
0 0 0 0 1 1 2 1 | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 | * * * * * * * * 5 * * *  lower {5}
0 0 0 0 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 | * * * * * * * * * 5 * *
0 0 0 0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 0 0 5 | * * * * * * * * * * * 1  bottom {5}

or
10  *  *  * |  2  1  1  0  0 0  0  0  0 0 | 1  2  1  0  0  0  polar
 * 10  *  * |  0  1  1  1  1 0  0  0  0 0 | 0  1  2  1  0  0  medial
 *  * 10  * |  0  0  0  1  0 1  1  1  1 0 | 0  0  1  1  2  1  tropal, opp. {5}
 *  *  * 10 |  0  0  0  0  1 0  1  1  1 1 | 0  0  1  1  1  2  tropal, opp. {3}
------------+-----------------------------+-----------------
 2  0  0  0 | 10  *  *  *  * *  *  *  * * | 1  1  0  0  0  0  polar
 1  1  0  0 |  * 10  *  *  * *  *  *  * * | 0  1  1  0  0  0
 1  1  0  0 |  *  * 10  *  * *  *  *  * * | 0  1  1  0  0  0
 0  1  1  0 |  *  *  * 10  * *  *  *  * * | 0  0  1  1  0  0
 0  1  0  1 |  *  *  *  * 10 *  *  *  * * | 0  0  1  1  0  0
 0  0  2  0 |  *  *  *  *  * 5  *  *  * * | 0  0  0  0  2  0
 0  0  1  1 |  *  *  *  *  * * 10  *  * * | 0  0  1  0  1  0  tropical {5},{3} joins
 0  0  1  1 |  *  *  *  *  * *  * 10  * * | 0  0  0  1  0  1  tropical {3},{3} joins
 0  0  1  1 |  *  *  *  *  * *  *  * 10 * | 0  0  0  0  1  1
 0  0  0  2 |  *  *  *  *  * *  *  *  * 5 | 0  0  0  0  0  2
------------+-----------------------------+-----------------
 5  0  0  0 |  5  0  0  0  0 0  0  0  0 0 | 2  *  *  *  *  * polar {5}
 2  1  0  0 |  1  1  1  0  0 0  0  0  0 0 | * 10  *  *  *  *
 1  2  1  1 |  0  1  1  1  1 0  1  0  0 0 | *  * 10  *  *  *  lateral {5}
 0  1  1  1 |  0  0  0  1  1 0  0  1  0 0 | *  *  * 10  *  *
 0  0  2  1 |  0  0  0  0  0 1  1  0  1 0 | *  *  *  * 10  *  equ. {3} adj. to {5}
 0  0  1  2 |  0  0  0  0  0 0  0  1  1 1 | *  *  *  *  * 10  equ. {3} adj. to {3}