Acronym	idhi
Name	invertidodecahedronary hecatonicosachoron
Cross sections	©
Circumradius	1
Coordinates	(1, 0, 0, 0)                                         & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2)                             & all permutations, all changes of sign (vertex inscribed tes) ((1+sqrt(5))/4, (sqrt(5)-1)/4, 1/4, 0)   & all even permutations, all changes of sign (vertex inscribed v-sadi)
General of army	ex
Colonel of regiment	sishi
Face vector	120, 1200, 1440, 120
Confer	Grünbaumian relatives: gaghi+idhi   sishi+gaghi+idhi   sishi+idhi   general polytopal classes: noble polytopes
External links

As abstract polytope idhi is automorphic, thereby interchanging the roles of pentagons and pentagrams. As such it could be seen to be a non-regular realization of the regular abstract polychoron {5,6,6}.

Incidence matrix

120 ♦   20 |  30  30 |  20
----+------+---------+----
  2 | 1200 |   3   3 |   6
----+------+---------+----
  5 |    5 | 720   * |   2  {5}
  5 |    5 |   * 720 |   2  {5/2}
----+------+---------+----
 20 |   60 |  12  12 | 120  ditdid