Acronym doaid, doe || id, K-4.77
Name dodecahedron atop icosidodecahedron,
dodecahedral cupola
Segmentochoron display
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
            o5x
               
x5o            
               
            f5o
               
               
               
f5o            
               
            x5x
               
o5f            
               
               
               
            o5f
               
o5x            
               
            x5o
Dihedral angles
  • at {3} between pap and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between pap and pap:   120°
  • at {5} between doe and pap:   108°
  • at {3} between id and tet:   arccos[(3-sqrt(5))/sqrt(32)] = 82.238756°
  • at {5} between id and pap:   72°
Confer
uniform relative:
ex  
related CRFs:
twau doaid  
general polytopal classes:
segmentochora   fundamental lace prisms  
External
links
polytopewiki  

As abstract polytope doaid is isomorphic to gissidagid, thereby replacing pentagons by pentagrams resp. replacing does by gissids, paps by staps, and ids by gids.

This monostratic polychoron could be obtained as a bistratic tropical section of ex, when all medial vertices would be diminished in addition (there chopping off a pappy each).


Incidence matrix according to Dynkin symbol

oo3ox5xo&#x   → height = (1+sqrt(5))/4 = 0.809017
(doe || id)

o.3o.5o.    | 20  * |  3  3  0 |  3  3  3  0  0 | 1  1  3 0
.o3.o5.o    |  * 30 |  0  2  4 |  0  4  1  2  2 | 0  2  2 1
------------+-------+----------+----------------+----------
.. .. x.    |  2  0 | 30  *  * |  2  0  1  0  0 | 1  0  2 0
oo3oo5oo&#x |  1  1 |  * 60  * |  0  2  1  0  0 | 0  1  2 0
.. .x ..    |  0  2 |  *  * 60 |  0  1  0  1  1 | 0  1  1 1
------------+-------+----------+----------------+----------
.. o.5x.    |  5  0 |  5  0  0 | 12  *  *  *  * | 1  0  1 0
.. ox ..&#x |  1  2 |  0  2  1 |  * 60  *  *  * | 0  1  1 0
.. .. xo&#x |  2  1 |  1  2  0 |  *  * 30  *  * | 0  0  2 0
.o3.x ..    |  0  3 |  0  0  3 |  *  *  * 20  * | 0  1  0 1
.. .x5.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
------------+-------+----------+----------------+----------
o.3o.5x.     20  0 | 30  0  0 | 12  0  0  0  0 | 1  *  * *
oo3ox ..&#x   1  3 |  0  3  3 |  0  3  0  1  0 | * 20  * *
.. ox5xo&#x   5  5 |  5 10  5 |  1  5  5  0  1 | *  * 12 *
.o3.x5.o      0 30 |  0  0 60 |  0  0  0 20 12 | *  *  * 1

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