Acronym | sissid | |||||||||||||||||||||||||||||||
TOCID symbol | D* | |||||||||||||||||||||||||||||||
Name |
small stellated dodecahedron, penta-stellahedron, vertex figure of gofix | |||||||||||||||||||||||||||||||
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VRML |
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Circumradius | sqrt[(5-sqrt(5))/8] = 0.587785 | |||||||||||||||||||||||||||||||
Inradius | sqrt[(5-sqrt(5))/40] = 0.262866 | |||||||||||||||||||||||||||||||
Density | 3 | |||||||||||||||||||||||||||||||
Vertex figure | [(5/2)5] | |||||||||||||||||||||||||||||||
Vertex layers |
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Lace city in approx. ASCII-art |
o o x v v x o o | |||||||||||||||||||||||||||||||
Coordinates |
(1/2, 1/2τ, 0) & even permutations, all changes of sign where τ = (1+sqrt(5))/2 | |||||||||||||||||||||||||||||||
General of army | ike | |||||||||||||||||||||||||||||||
Colonel of regiment | (is itself locally convex – other uniform polyhedral member: gike – other edge facetings) | |||||||||||||||||||||||||||||||
Dual | gad | |||||||||||||||||||||||||||||||
Dihedral angles |
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Face vector | 12, 30, 12 | |||||||||||||||||||||||||||||||
Confer |
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External links |
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As abstract polytope sissid is isomorphic to gad, thereby replacing facial pentagrams by pentagons and conversely vertex figure pentagons by corresponding pentagrams. Both sissid and gad can be seen as different realizations of the same self-dual regular abstract polyhedron {5,5}6 (where the index just denotes the size of the corresponding Petrie polygon) which in turn equates to the representation {5,5|3} = x5o5o | x3o (where that suffix then denotes the size of the corresponding hole). In fact, the latter occurs here as face of the inscribed gike.
Incidence matrix according to Dynkin symbol
x5/2o5o . . . | 12 | 5 | 5 --------+----+----+--- x . . | 2 | 30 | 2 --------+----+----+--- x5/2o . | 5 | 5 | 12 snubbed forms: β5/2o5o
x5/3o5o . . . | 12 | 5 | 5 --------+----+----+--- x . . | 2 | 30 | 2 --------+----+----+--- x5/3o . | 5 | 5 | 12
o5/4o5/2x . . . | 12 | 5 | 5 ----------+----+----+--- . . x | 2 | 30 | 2 ----------+----+----+--- . o5/2x | 5 | 5 | 12
o5/4o5/3x . . . | 12 | 5 | 5 ----------+----+----+--- . . x | 2 | 30 | 2 ----------+----+----+--- . o5/3x | 5 | 5 | 12
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