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 cityin 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 Externallinks

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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