Acronym sissidadid, sissid || did
Name small stellated dodecahedron atop dodecadodecahedron,
small-stellated-dodecahedral cupola
Circumradius sqrt[(8+2 sqrt(5))/11] = 1.064815
Dihedral angles
  • at {5/2} between sissid and stap:   arccos(-sqrt[sqrt(5)/4]) = 138.389326°
  • at {5} between did and peppy:   arccos(sqrt[(9-4 sqrt(5))/4]) = 83.221348°
  • at {5/2} between did and stap:   arccos(sqrt[sqrt(5)/4]) = 41.610674°
  • at {3} between peppy and stap:   ...
  • at {3} between stap and stap:   ...
Confer
orbiform relative:
sidrebcu  
general polytopal classes:
segmentochora  

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


Incidence matrix according to Dynkin symbol

xo5/2ox5oo&#x   → height = sqrt[(5 sqrt(5)-9)/8] = 0.522056
(sissid || did)

o.5/2o.5o.    | 12  * |  5  5  0 |  5  5  5  0  0 | 1  5  1 0
.o5/2.o5.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
oo5/2oo5oo&#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.5/2o. ..    |  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
.o5/2.x ..    |  0  5 |  0  0  5 |  *  *  * 12  * | 0  1  0 1
..   .x5.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
--------------+-------+----------+----------------+----------
x.5/2o.5o.     12  0 | 30  0  0 | 12  0  0  0  0 | 1  *  * *
xo5/2ox ..&#x   5  5 |  5 10  5 |  1  5  5  1  0 | * 12  * *
..   ox5oo&#x   1  5 |  0  5  5 |  0  0  5  0  1 | *  * 12 *
.o5/2.x5.o      0 30 |  0  0 60 |  0  0  0 12 12 | *  *  * 1

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