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°
Face vector	50, 150, 134, 34
Confer	uniform relative: ex   related CRFs: twau doaid   general polytopal classes: segmentochora   fundamental lace prisms
External links

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