Acronym ..., 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[7+3sqrt(5)]/4) = 157.761244°
  • at {3} between pap and pap:   120°
  • at {5} between doe and pap:   108°
  • at {3} between tet and id:   arccos[(3-sqrt(5))/sqrt(32)] = 82.238756°
  • at {5} between id and pap:   72°
Confer
uniform relative:
ex  

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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