Acronym gaddadid, gad || did
Name great dodecahedron atop dodecadodecahedron,
great-dodecahedral cupola
Circumradius sqrt[(8+2 sqrt(5))/11] = 1.064815
Dihedral angles
  • at {5} between gad and pap:   arccos(-sqrt[(9-4 sqrt(5))/4]) = 96.778652°
  • at {5} between did and pap:   arccos(sqrt[(9-4 sqrt(5))/4]) = 83.221348°
  • at {5/2} between did and stappy:   arccos(sqrt[(9-4 sqrt(5))/4]) = 83.221348°
  • at {3} between pap and pap:   ...
  • at {3} between pap and stappy:   ...
Confer
orbiform relative:
sidrebcu  
general polytopal classes:
segmentochora  

As abstract polytope gaddadid is isomorphic to sissidadid, thereby interchanging pentagons and pentagrams resp. replacing gads by sissids, stappies by peppies, and paps by staps.


Incidence matrix according to Dynkin symbol

xo5ox5/2oo&#x   → height = sqrt[(3 sqrt(5)-1)/8] = 0.844704
(gad || did)

o.5o.5/2o.    | 12  * |  5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o5.o5/2.o    |  * 30 |  0  2  4 |  0  1  4  2  2 | 0  2  2 1
--------------+-------+----------+----------------+----------
x. ..   ..    |  2  0 | 30  *  * |  2  1  0  0  0 | 1  2  0 0
oo5oo5/2oo&#x |  1  1 |  * 60  * |  0  1  2  0  0 | 0  2  1 0
.. .x   ..    |  0  2 |  *  * 60 |  0  0  1  1  1 | 0  1  1 1
--------------+-------+----------+----------------+----------
x.5o.   ..    |  5  0 |  5  0  0 | 12  *  *  *  * | 1  1  0 0
xo ..   ..&#x |  2  1 |  1  2  0 |  * 30  *  *  * | 0  2  0 0
.. ox   ..&#x |  1  2 |  0  2  1 |  *  * 60  *  * | 0  1  1 0
.o5.x   ..    |  0  5 |  0  0  5 |  *  *  * 12  * | 0  1  0 1
.. .x5/2.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
--------------+-------+----------+----------------+----------
x.5o.5/2o.     12  0 | 30  0  0 | 12  0  0  0  0 | 1  *  * *
xo5ox   ..&#x   5  5 |  5 10  5 |  1  5  5  1  0 | * 12  * *
.. ox5/2oo&#x   1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o5.x5/2.o      0 30 |  0  0 60 |  0  0  0 12 12 | *  *  * 1

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