Acronym sishi
Name small stellated hecatonicosachoron
Cross sections
 ©
Circumradius 1
Inradius (1+sqrt(5))/4 = 0.809017
General of army ex
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: co ditdid gad gidtid gike ike oct oho pip sidtid sissid stip tet thah trip
sadixhix (compound) 3000000000000006000
gadixhix (compound) 3000000000000006000
idhi 01200000000000000
gaghi 00120000000000000
didhi 0001201200000000000
gitpodady (fissary) 0001200120000000000
sridixhi 0001200000000060000
dittady 0000120120000000000
sifdahihox (fissary) 0000120003000000000
sitpodady (fissary) 0000120000012000000
sidtixhi 0000120000000060000
sridaphi 00001200000000001200
gifdahihox (fissary) 0000012003000000000
ofiddady 0000012000012000000
gidtixhi 0000012000000060000
gridaphi 00000120000000001200
dox (compound) 00000060000000000
paphacki 00000000720000000
gridixhi 0000000001200060000
sishi 00000000001200000
paphicki 00000000000720000
& others)
Dual fix
Dihedral angles
Confer
Grünbaumian relatives:
sishi+gaghi+120did   sishi+gaghi+idhi   sishi+gridixhi   sishi+idhi   sishi+ofiddady   sishi+paphicki+gridaphi   2sishi   2sishi+2paphicki  
uniform relative:
gudap  
decompositions:
pt || sishi  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   WikiChoron   nan ma

As abstract polytope sishi is isomorphic to gaghi, thereby replacing pentagrams by pentagons, resp. sissid by gad, resp. replacing doe vertex figures by gissid ones.

Here the sissids form 12 swirling rings of 10 each.

Note that the edge skeleton supports not only sissid or gike cells, but also gad or ike cells. Therefore any single such ring of 10 sissids could well be replaced by a ring of starps (5/3-antiprisms). The then open faces could be closed by a complemental ring of 10 paps (5-antiprisms) – up to some "glue" of 50 tets: This is how gudap could be obtained herefrom as a subsymmetrical faceting.

If considered with according densities, then sishi can be thought of as the external blend of 120 sissidpies. This decomposition is described as the degenerate segmentoteron ox5/2oo5oo3oo&#x.


Incidence matrix according to Dynkin symbol

x5/2o5o3o

.   . . . | 120    20 |  30 |  12
----------+-----+------+-----+----
x   . . . |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
x5/2o . . |   5 |    5 | 720 |   2
----------+-----+------+-----+----
x5/2o5o .   12 |   30 |  12 | 120

x5/2o5o3/2o

.   . .   . | 120    20 |  30 |  12
------------+-----+------+-----+----
x   . .   . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5/2o .   . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5/2o5o   .   12 |   30 |  12 | 120

x5/2o5/4o3o

.   .   . . | 120    20 |  30 |  12
------------+-----+------+-----+----
x   .   . . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5/2o   . . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5/2o5/4o .   12 |   30 |  12 | 120

x5/2o5/4o3/2o

.   .   .   . | 120    20 |  30 |  12
--------------+-----+------+-----+----
x   .   .   . |   2 | 1200 |   3 |   3
--------------+-----+------+-----+----
x5/2o   .   . |   5 |    5 | 720 |   2
--------------+-----+------+-----+----
x5/2o5/4o   .   12 |   30 |  12 | 120

x5/3o5o3o

.   . . . | 120    20 |  30 |  12
----------+-----+------+-----+----
x   . . . |   2 | 1200 |   3 |   3
----------+-----+------+-----+----
x5/3o . . |   5 |    5 | 720 |   2
----------+-----+------+-----+----
x5/3o5o .   12 |   30 |  12 | 120

x5/3o5o3/2o

.   . .   . | 120    20 |  30 |  12
------------+-----+------+-----+----
x   . .   . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5/3o .   . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5/3o5o   .   12 |   30 |  12 | 120

x5/3o5/4o3o

.   .   . . | 120    20 |  30 |  12
------------+-----+------+-----+----
x   .   . . |   2 | 1200 |   3 |   3
------------+-----+------+-----+----
x5/3o   . . |   5 |    5 | 720 |   2
------------+-----+------+-----+----
x5/3o5/4o .   12 |   30 |  12 | 120

x5/3o5/4o3/2o

.   .   .   . | 120    20 |  30 |  12
--------------+-----+------+-----+----
x   .   .   . |   2 | 1200 |   3 |   3
--------------+-----+------+-----+----
x5/3o   .   . |   5 |    5 | 720 |   2
--------------+-----+------+-----+----
x5/3o5/4o   .   12 |   30 |  12 | 120

© 2004-2019
top of page