Acronym ikadoe (alt.: ikap), ike || doe, K-4.78
Name icosahedron atop dodecahedron,
icosahedral antiprism,
dodecahedral antiprism,
segment of vertex-first hexacosachoron
 
Segmentochoron display
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
  o5o  o5x      x5o  o5o  
                          
x5o      f5o  o5f      o5x
       x3o   o3f f3o   o3x       
                                 
                                 
o3o o3f   f3x       x3f   f3o o3o
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between ike and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between peppy and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {5} between doe and peppy:   72°
Confer
uniform relative:
ex  
related segmentochora:
papadoe   teddi adoe   mibdiadoe   gissid-gike retroprism   gissid-gike antiprism  
general polytopal classes:
segmentochora   fundamental lace prisms  
External
links
polytopewiki  

As abstract polytope ikadoe is isomorphic to both, the gissid-gike antiprism and the gissid-gike retroprism, both having then exactly the same incidences but different heights. Thereby it replaces pentagons by pentagrams resp. does by gissids, ikes by gikes, and peppies by stappies. In the taller one of those, the antiprism, the first type vertex figure acts in turn as a pentagonal antiprism variant, and in the narrower one, the gissid-gike retroprism, that vertex figure is as a pentagonal retroprism variant instead. Thence ikadoe then will be the conjugate to that gissid-gike retroprism.

The analysis of the being used lacing facets shows that the half-height section results in a half-edge sized srid.


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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