Acronym  sishiap 
Name 
small stellated hecatonicosachoron antiprism, narrower sishi atop sishi 
Circumradius  sqrt[(7+sqrt(5))/8] = 1.074481 
Confer 

Top and bottom is an alike oriented sishi each. But its height is a bit smaller than for the siship. The staps run between directly aligned underneath pentagrams, resp. hossdaps run between directly aligned underneath sissids.
The vertex figure of sishiap is a variant of the reduced version of xv5/2ov5oo&#x (omitting a doublecover from its Grünbaumian bottom base).
This polyteron could be obtained itself as an accordingly reduced form of β2β5o5/2o5o, then omitting a doublecover from its Grünbaumian 3sishi (?) bases, leaving a simple sishi instead.
narrower sishi  sishi → height = sqrt[(sqrt(5)1)/2] = 0.786151
240  12 20  90 30  30 72 12  12 1 13
++++
2  1440 *  10 0  5 10 0  5 0 2
2  * 2400  3 3  3 6 3  3 1 3
++++
3  2 1  7200 *  1 2 0  2 0 1
5  0 5  * 1440  1 2 2  2 1 2 {5/2}
++++
10  10 10  10 2  720 * *  2 0 0 stap
6  5 5  5 1  * 2880 *  1 0 1 stappy
12  0 30  0 12  * * 240  0 1 1 sissid
++++
24  60 60  120 24  12 24 0  120 * * hossdap
120  0 1200  0 720  0 0 120  * 2 * sishi
13  12 30  30 12  0 12 1  * * 240 sissidpy
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