Acronym	sissidagad, sissid || gad
Name	small stellated decahedron atop great dodecahedron, sissid antiprism, gad antiprism
Circumradius	1
Face vector	24, 120, 144, 56
Confer	general polytopal classes: segmentochora
External links

As abstract polytope sissidagad is automorph, thereby interchanging the roles of pentagons and pentagrams, resp. those of stappy and peppy.

Incidence matrix according to Dynkin symbol

xo5/2oo5ox&#x   → height = 1/2
(sissid || gad)

o.5/2o.5o.    | 12  * |  5  5  0 |  5 10  5  0 | 1  5  5  1 0
.o5/2.o5.o    |  * 12 |  0  5  5 |  0  5 10  5 | 0  1  5  5 1
--------------+-------+----------+-------------+-------------
x.   .. ..    |  2  0 | 30  *  * |  2  2  0  0 | 1  2  1  0 0
oo5/2oo5oo&#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.5/2o. ..    |  5  0 |  5  0  0 | 12  *  *  * | 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.5/2o.5o.    ♦ 12  0 | 30  0  0 | 12  0  0  0 | 1  *  *  * *
xo5/2oo ..&#x ♦  5  1 |  5  5  0 |  1  5  0  0 | * 12  *  * *
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 *
.o5/2.o5.x    ♦  0 12 |  0  0 30 |  0  0  0 12 | *  *  *  * 1