Acronym qrid
TOCID symbol rJE*
Name quasi rhombicosidodecahedron,
great (non-convex) rhombicosidodecahedron (i.e. not grid)
 
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Circumradius sqrt[-sqrt(5)+11/4] = 0.716891
Vertex figure [5/3,4,3,4]
General of army f3x5o
Colonel of regiment gaddid
Dihedral angles
  • between {3} and {4}:   arccos((sqrt(5)-1)/sqrt(12)) = 69.094843°
  • between {4} and {5/2}:   arccos(sqrt[(5-sqrt(5))/10]) = 58.282526°
Face vector 60, 120, 62
Confer
non-convex cap:
rastacu  
related polyhedra:
gibil biro   githawro  
general polytopal classes:
Wythoffian polyhedra  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   mathworld

As abstract polytope qrid is isomorphic to srid, thereby replacing retrograde pentagrams by prograde pentagons. – As such qrid is a lieutenant.

Just as the lunes of srid had been reused in bilbiro and thawro, the more folded lunes of this conjugate polyhedron are being reused in their conjugates as well, i.e. in gibil biro and githawro.

This polyhedron is an edge-faceting of the great dodekicosidodecahedron (gaddid).


Incidence matrix according to Dynkin symbol

x5/3o3x

.   . . | 60 |  2  2 |  1  2  1
--------+----+-------+---------
x   . . |  2 | 60  * |  1  1  0
.   . x |  2 |  * 60 |  0  1  1
--------+----+-------+---------
x5/3o . |  5 |  5  0 | 12  *  *
x   . x |  4 |  2  2 |  * 30  *
.   o3x |  3 |  0  3 |  *  * 20

x3/2o5/2x

.   .   . | 60 |  2  2 |  1  2  1
----------+----+-------+---------
x   .   . |  2 | 60  * |  1  1  0
.   .   x |  2 |  * 60 |  0  1  1
----------+----+-------+---------
x3/2o   . |  3 |  3  0 | 20  *  *
x   .   x |  4 |  2  2 |  * 30  *
.   o5/2x |  5 |  0  5 |  *  * 12

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