Acronym ..., ike || doe, K-4.78
Name icosahedron atop dodecahedron,
icosahedral antiprism,
dodecahedral antiprism
 
Segmentochoron display
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
  o5o  o5x      x5o  o5o  
                          
x5o      f5o  o5f      o5x
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between ike and tet:   arccos(-sqrt[7+3sqrt(5)]/4) = 157.761244°
  • at {3} between peppy and tet:   arccos(-sqrt[7+3sqrt(5)]/4) = 157.761244°
  • at {5} between doe and peppy:   72°
Confer
uniform relative:
ex  

This one also happens to be the second stratum of ex in vertex first orientation.


Incidence matrix according to Dynkin symbol

xo3oo5ox&#x   → height = 1/2
(ike || doe)


o.3o.5o.    | 12  *   5  5  0 |  5 10  5  0 | 1  5  5  1 0
.o3.o5.o    |  * 20 |  0  3  3 |  0  3  6  3 | 0  1  3  3 1
------------+-------+----------+-------------+-------------
x. .. ..    |  2  0 | 30  *  * |  2  2  0  0 | 1  2  1  0 0
oo3oo5oo&#x |  1  1 |  * 60  * |  0  2  2  0 | 0  1  2  1 0
.. .. .x    |  0  2 |  *  * 30 |  0  0  2  2 | 0  0  1  2 1
------------+-------+----------+-------------+-------------
x.3o. ..    |  3  0 |  3  0  0 | 20  *  *  * | 1  1  0  0 0
xo .. ..&#x |  2  1 |  1  2  0 |  * 60  *  * | 0  1  1  0 0
.. .. ox&#x |  1  2 |  0  2  1 |  *  * 60  * | 0  0  1  1 0
.. .o5.x    |  0  5 |  0  0  5 |  *  *  * 12 | 0  0  0  1 1
------------+-------+----------+-------------+-------------
x.3o.5o.     12  0 | 30  0  0 | 20  0  0  0 | 1  *  *  * *
xo3oo ..&#x   3  1 |  3  3  0 |  1  3  0  0 | * 20  *  * *
xo .. ox&#x   2  2 |  1  4  1 |  0  2  2  0 | *  * 30  * *
.. oo5ox&#x   1  5 |  0  5  5 |  0  0  5  1 | *  *  * 12 *
.o3.o5.x      0 20 |  0  0 30 |  0  0  0 12 | *  *  *  * 1

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