Acronym	doasrid, doe || srid, K-4.152
Name	dodecahedron atop small rhombicosidodecahedron, dodecahedral cap of small disprismatohexacosihecatonicosachoron
Segmentochoron display
Circumradius	3+sqrt(5) = 5.236068
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	at {3} between tet and trip:   arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756° at {4} between pip and trip:   arccos(-sqrt[(10+2 sqrt(5))/15]) = 169.187683° at {5} between doe and pip:   162° at {3} between srid and tet:   arccos(sqrt[7+3 sqrt(5)]/4) = 22.238756° at {4} between srid and trip:   arccos(sqrt[(3+sqrt(5))/6]) = 20.905157° at {5} between pip and srid:   18°
Face vector	80, 210, 194, 64
Confer	uniform relative: sidpixhi   related segmentochora: doa pabidrid   general polytopal classes: segmentochora
External links

Incidence matrix according to Dynkin symbol

ox3oo5xx&#x   → height = (sqrt(5)-1)/4 = 0.309017
(doe || srid)

o.3o.5o.    | 20  * |  3  3  0  0 |  3  3  6  0  0  0 | 1  1  3  3 0
.o3.o5.o    |  * 60 |  0  1  2  2 |  0  2  2  1  2  1 | 0  1  2  1 1
------------+-------+-------------+-------------------+-------------
.. .. x.    |  2  0 | 30  *  *  * |  2  0  2  0  0  0 | 1  0  1  2 0
oo3oo5oo&#x |  1  1 |  * 60  *  * |  0  2  2  0  0  0 | 0  1  2  1 0
.x .. ..    |  0  2 |  *  * 60  * |  0  1  0  1  1  0 | 0  1  1  0 1
.. .. .x    |  0  2 |  *  *  * 60 |  0  0  1  0  1  1 | 0  0  1  1 1
------------+-------+-------------+-------------------+-------------
.. o.5x.    |  5  0 |  5  0  0  0 | 12  *  *  *  *  * | 1  0  0  1 0
ox .. ..&#x |  1  2 |  0  2  1  0 |  * 60  *  *  *  * | 0  1  1  0 0
.. .. xx&#x |  2  2 |  1  2  0  1 |  *  * 60  *  *  * | 0  0  1  1 0
.x3.o ..    |  0  3 |  0  0  3  0 |  *  *  * 20  *  * | 0  1  0  0 1
.x .. .x    |  0  4 |  0  0  2  2 |  *  *  *  * 30  * | 0  0  1  0 1
.. .o5.x    |  0  5 |  0  0  0  5 |  *  *  *  *  * 12 | 0  0  0  1 1
------------+-------+-------------+-------------------+-------------
o.3o.5x.    ♦ 20  0 | 30  0  0  0 | 12  0  0  0  0  0 | 1  *  *  * *
ox3oo ..&#x ♦  1  3 |  0  3  3  0 |  0  3  0  1  0  0 | * 20  *  * *
ox .. xx&#x ♦  2  4 |  1  4  2  2 |  0  2  2  0  1  0 | *  * 30  * *
.. oo5xx&#x ♦  5  5 |  5  5  0  5 |  1  0  5  0  0  1 | *  *  * 12 *
.x3.o5.x    ♦  0 60 |  0  0 60 60 |  0  0  0 20 30 12 | *  *  *  * 1