Acronym	gishi, gspD
Name	great stellated hecatonicosachoron, greatened stellated polydodecahedron
Cross sections	©
Circumradius	(sqrt(5)-1)/2 = 0.618034
Inradius	(sqrt(5)-1)/4 = 0.309017
Density	20
General of army	ex
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: gike gissid sissid tet gishi 0 120 0 0 gashi 0 0 120 0 gax 0 0 0 600 gofix 120 0 0 0 & others)
Dual	gahi
Dihedral angles	at {5/2} between gissid and gissid:   144°
Face vector	120, 720, 720, 120
Confer	Grünbaumian relatives: gishi+gashi   2gishi   related scaliform: gisp   gypasp   general polytopal classes: Wythoffian polychora   regular   noble polytopes
External links

As abstract polytope gishi is isomorphic to gahi, thereby replacing gissid by doe, resp. replacing pentagrammal faces by pentagonal ones, resp. replacing pentagonal edge figures each by pentagrammal ones, resp. replacing ike vertex figures by gike ones.

Both gishi and gahi can be seen as different realizations of the same self-dual regular abstract polychoron {5,3,5|3} = x5o3o5o | x3o (where the suffix denotes the size of the corresponding hole). In fact, the latter occurs here as face of the inscribed gax.

Incidence matrix according to Dynkin symbol

o5o3o5/2x

. . .   . | 120 ♦  12 |  30 |  20
----------+-----+-----+-----+----
. . .   x |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
. . o5/2x |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
. o3o5/2x ♦  20 |  30 |  12 | 120

o5o3o5/3x

. . .   . | 120 ♦  12 |  30 |  20
----------+-----+-----+-----+----
. . .   x |   2 | 720 |   5 |   5
----------+-----+-----+-----+----
. . o5/3x |   5 |   5 | 720 |   2
----------+-----+-----+-----+----
. o3o5/3x ♦  20 |  30 |  12 | 120

o5o3/2o5/2x

. .   .   . | 120 ♦  12 |  30 |  20
------------+-----+-----+-----+----
. .   .   x |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
. .   o5/2x |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
. o3/2o5/2x ♦  20 |  30 |  12 | 120

o5o3/2o5/3x

. .   .   . | 120 ♦  12 |  30 |  20
------------+-----+-----+-----+----
. .   .   x |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
. .   o5/3x |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
. o3/2o5/3x ♦  20 |  30 |  12 | 120

o5/4o3o5/2x

.   . .   . | 120 ♦  12 |  30 |  20
------------+-----+-----+-----+----
.   . .   x |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
.   . o5/2x |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
.   o3o5/2x ♦  20 |  30 |  12 | 120

o5/4o3o5/3x

.   . .   . | 120 ♦  12 |  30 |  20
------------+-----+-----+-----+----
.   . .   x |   2 | 720 |   5 |   5
------------+-----+-----+-----+----
.   . o5/3x |   5 |   5 | 720 |   2
------------+-----+-----+-----+----
.   o3o5/3x ♦  20 |  30 |  12 | 120

o5/4o3/2o5/2x

.   .   .   . | 120 ♦  12 |  30 |  20
--------------+-----+-----+-----+----
.   .   .   x |   2 | 720 |   5 |   5
--------------+-----+-----+-----+----
.   .   o5/2x |   5 |   5 | 720 |   2
--------------+-----+-----+-----+----
.   o3/2o5/2x ♦  20 |  30 |  12 | 120

o5/4o3/2o5/3x

.   .   .   . | 120 ♦  12 |  30 |  20
--------------+-----+-----+-----+----
.   .   .   x |   2 | 720 |   5 |   5
--------------+-----+-----+-----+----
.   .   o5/3x |   5 |   5 | 720 |   2
--------------+-----+-----+-----+----
.   o3/2o5/3x ♦  20 |  30 |  12 | 120