Acronym	sishia
Name	small stellated hecatonicosachoron alterprism, narrower sishi atop sishi
Circumradius	sqrt[(7+sqrt(5))/8] = 1.074481
Face vector	240, 3840, 8640, 3840, 362
uniform relative: siship   Grünbaumian relatives: β2β5o5/2o5o   general polytopal classes: scaliform
External links

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 sishia is a variant of the reduced version of xv5/2ov5oo&#x (omitting a double-cover from its Grünbaumian bottom base).

This polyteron could be obtained itself as an accordingly reduced form of β2β5o5/2o5o, then omitting a double-cover from its Grünbaumian 3sishi bases, leaving a simple sishi instead.

Incidence matrix

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