Acronym	gadadoe
Name	great dodecahedron atop dodecahedron
Circumradius	(1+sqrt(5))/2 = 1.618034
Vertex figures	,
Face vector	32, 120, 142, 44
Confer	uniform relative: ex   general polytopal classes: segmentochora

As abstract polytope gadadoe is isomorph to gissidasissid, therby replacing gad by sissid, doe by gissid, and pap by starp.

Its vertex figures above are displayed to be faceting of ike. Therfrom it becomes evident that this polychoron itself occurs as an edge-faceting within ex.

It was found by the author in early 2023 shortly after Mecejide's find of gikaike.

Incidence matrix

gad || doe   → height = 1/2

12  * |  5  5  0 |  5 10  5  0 | 1  5  5 0
 * 20 |  0  3  3 |  0  3  6  3 | 0  3  3 1
------+----------+-------------+----------
 2  0 | 30  *  * |  2  2  0  0 | 1  2  1 0
 1  1 |  * 60  * |  0  2  2  0 | 0  2  2 0
 0  2 |  *  * 30 |  0  0  2  2 | 0  2  1 1
------+----------+-------------+----------
 5  0 |  5  0  0 | 12  *  *  * | 1  1  0 0
 2  1 |  1  2  0 |  * 60  *  * | 0  1  1 0
 1  2 |  0  2  1 |  *  * 60  * | 0  1  1 0
 0  5 |  0  0  5 |  *  *  * 12 | 0  1  0 1
------+----------+-------------+----------
12  0 | 30  0  0 | 12  0  0  0 | 1  *  * * gad
 5  5 |  5 10  5 |  1  5  5  1 | * 12  * * pap
 2  2 |  1  4  1 |  0  2  2  0 | *  * 30 * tet
 0 20 |  0  0 30 |  0  0  0 12 | *  *  * 1 doe