Acronym	pero, J6
Name	pentagonal rotunda, half of icosidodecahedron
VRML	⭳ ©
Circumradius	(1+sqrt(5))/2 = 1.618034
Vertex figure	[(3,5)2], [3,5,10]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {5}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632° between {3} and {10}:   arccos(sqrt[(5-2 sqrt(5))/15]) = 79.187683° between {5} and {10}:   arccos(1/sqrt(5)) = 63.434949°
Face vector	20, 35, 17
Confer	related Johnson solids: gyepro   pocuro   pocuro   pobro   epgybro   uniform relative: id   other symmetries vov3ofx&#xt   general polytopal classes: Johnson solids   bistratic lace towers
External links

This polyhedron is an edge-faceting of the icosidodecahedron (id).

As abstract polytope pero is isomorphic to sisro, thereby replacing pentagons by pentagrams and the prograde decagon by a retrograde decagram.

Incidence matrix according to Dynkin symbol

xox5ofx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/10] = 0.525731
                height(2,3) = sqrt[(5+sqrt(5))/10] = 0.850651
({5} || pseudo dual f-{5} || {10})

o..5o..     | 5 *  * | 2  2  0 0 0 | 1 2 1 0 0
.o.5.o.     | * 5  * | 0  2  2 0 0 | 0 1 2 1 0
..o5..o     | * * 10 | 0  0  1 1 1 | 0 0 1 1 1
------------+--------+-------------+----------
x.. ...     | 2 0  0 | 5  *  * * * | 1 1 0 0 0
oo.5oo.&#x  | 1 1  0 | * 10  * * * | 0 1 1 0 0
.oo5.oo&#x  | 0 1  1 | *  * 10 * * | 0 0 1 1 0
..x ...     | 0 0  2 | *  *  * 5 * | 0 0 0 1 1
... ..x     | 0 0  2 | *  *  * * 5 | 0 0 1 0 1
------------+--------+-------------+----------
x..5o..     | 5 0  0 | 5  0  0 0 0 | 1 * * * *
xo. ...&#x  | 2 1  0 | 1  2  0 0 0 | * 5 * * *
... ofx&#xt | 1 2  2 | 0  2  2 0 1 | * * 5 * *
.ox ...&#x  | 0 1  2 | 0  0  2 1 0 | * * * 5 *
..x5..x     | 0 0 10 | 0  0  0 5 5 | * * * * 1