Replenished great icosahedron-small stellated dodecahedron morpher

Replenished great icosahedron-small stellated dodecahedron morpher
(OFF file)
Rank	3
Type	Orbiform
Notation
Bowers style acronym	Rigsisdom
Elements
Faces	5 triangles, 1+1+5 pentagrams
Edges	5+5+5+10
Vertices	1+5+5
Vertex figures	1 pentagon, edge length (√5–1)/2
	5 isosceles trapezoids, edge lengths 1, (√5–1)/2, (√5–1)/2, (√5–1)/2
	5 nonconvex pentagons, edge lengths 1, (√5–1)/2, (√5–1)/2, 1, (√5–1)/2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779$
Volume	${\frac {13{\sqrt {5}}-25}{24}}\approx 0.16954$
Dihedral angles	5/2–5/2: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	3-5/2: $\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }$
Related polytopes
Army	Gyepip, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Regiment	Regi
Conjugate	Diminished icosahedron-great dodecahedron morpher
Abstract & topological properties
Flag count	100
Orientable	Yes
Properties
Symmetry	H2×I, order 10
Convex	No
Nature	Tame

The replenished great icosahedron-small stellated dodecahedron morpher or rigsisdom, also called the replenished gike-sissid morpher, is a nonconvex orbiform polyhedron and an edge faceting of the small stellated dodecahedron. Its faces are 5 triangles and 1+1+5 pentagrams. It can be constructed from the great icosahedron-small stellated dodecahedron morpher by diminishing its great icosahedral vertex.

Vertex coordinates

Its vertex coordinates are the same as those of the small stellated dodecahedron with any one vertex removed.

External links

• Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#6 under sissid).