Acronym doa iddip
Name dodecahedron atop icosidodecahedron-prism
Circumradius sqrt[(13+5 sqrt(5))/8] = 1.738546
Lace city
in approx. ASCII-art
    o3o5x    
             
o3x5o   o3x5o
Face vector 80, 300, 376, 189, 35
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

ox oo3ox5xo&#x   → height = sqrt[(1+sqrt(5))/8] = 0.636010
(doe || iddip)

o. o.3o.5o.    | 20  * |  3   6  0   0 |  3  3   6  6  0  0  0 | 1  3  3  2  6  0  0 0 |  1  3 2 0
.o .o3.o5.o    |  * 60 |  0   2  1   4 |  0  2   4  1  4  2  2 | 0  4  1  2  2  2  2 1 |  2  2 1 1
---------------+-------+---------------+-----------------------+-----------------------+----------
.. .. .. x.    |  2  0 | 30   *  *   * |  2  0   0  2  0  0  0 | 1  0  1  0  4  0  0 0 |  0  2 2 0
oo oo3oo5oo&#x |  1  1 |  * 120  *   * |  0  1   2  1  0  0  0 | 0  2  1  1  2  0  0 0 |  1  2 1 0
.x .. .. ..    |  0  2 |  *   * 30   * |  0  2   0  0  4  0  0 | 0  4  1  0  0  2  2 0 |  2  2 0 1
.. .. .x ..    |  0  2 |  *   *  * 120 |  0  0   1  0  1  1  1 | 0  1  0  1  1  1  1 1 |  1  1 1 1
---------------+-------+---------------+-----------------------+-----------------------+----------
.. .. o.5x.    |  5  0 |  5   0  0   0 | 12  *   *  *  *  *  * | 1  0  0  0  2  0  0 0 |  0  1 2 0
ox .. .. ..&#x |  1  2 |  0   2  1   0 |  * 60   *  *  *  *  * | 0  2  1  0  0  0  0 0 |  1  2 0 0
.. .. ox ..&#x |  1  2 |  0   2  0   1 |  *  * 120  *  *  *  * | 0  1  0  1  1  0  0 0 |  1  1 1 0
.. .. .. xo&#x |  2  1 |  1   2  0   0 |  *  *   * 60  *  *  * | 0  0  1  0  2  0  0 0 |  0  2 1 0
.x .. .x ..    |  0  4 |  0   0  2   2 |  *  *   *  * 60  *  * | 0  1  0  0  0  1  1 0 |  1  1 0 1
.. .o3.x ..    |  0  3 |  0   0  0   3 |  *  *   *  *  * 40  * | 0  0  0  1  0  1  0 1 |  1  0 1 1
.. .. .x5.o    |  0  5 |  0   0  0   5 |  *  *   *  *  *  * 24 | 0  0  0  0  1  0  1 1 |  0  1 1 1
---------------+-------+---------------+-----------------------+-----------------------+----------
.. o.3o.5x.     20  0 | 30   0  0   0 | 12  0   0  0  0  0  0 | 1  *  *  *  *  *  * * |  0  0 2 0
ox .. ox ..&#x   1  4 |  0   4  2   2 |  0  2   2  0  1  0  0 | * 60  *  *  *  *  * * |  1  1 0 0
ox .. .. xo&#x   2  2 |  1   4  1   0 |  0  2   0  2  0  0  0 | *  * 30  *  *  *  * * |  0  2 0 0
.. oo3ox ..&#x   1  3 |  0   3  0   3 |  0  0   3  0  0  1  0 | *  *  * 40  *  *  * * |  1  0 1 0
.. .. ox5xo&#x   5  5 |  5  10  0   5 |  1  0   5  5  0  0  1 | *  *  *  * 24  *  * * |  0  1 1 0
.x .o3.x ..      0  6 |  0   0  3   6 |  0  0   0  0  3  2  0 | *  *  *  *  * 20  * * |  1  0 0 1
.x .. .x5.o      0 10 |  0   0  5  10 |  0  0   0  0  5  0  2 | *  *  *  *  *  * 12 * |  0  1 0 1
.. .o3.x5.o      0 30 |  0   0  0  60 |  0  0   0  0  0 20 12 | *  *  *  *  *  *  * 2 |  0  0 1 1
---------------+-------+---------------+-----------------------+-----------------------+----------
ox oo3ox ..&#x   1  6 |  0   6  3   6 |  0  3   6  0  3  2  0 | 0  3  0  2  0  1  0 0 | 20  * * *
ox .. ox5xo&#x   5 10 |  5  20  5  10 |  1 10  10 10  5  0  2 | 0  5  5  0  2  0  1 0 |  * 12 * *
.. oo3ox5xo&#x  20 30 | 30  60  0  60 | 12  0  60 30  0 20 12 | 1  0  0 20 12  0  0 1 |  *  * 2 *
.x .o3.x5.o      0 60 |  0   0 30 120 |  0  0   0  0 60 40 24 | 0  0  0  0  0 20 12 2 |  *  * * 1

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