Pentagrammic cupolaic blend

Pentagrammic cupolaic blend
Rank	3
Type	Segmentotope
Elements
Faces	10 triangles 10 squares 2 pentagrams as 1 stellated decagram
Edges	10+10+20
Vertices	10+10
Vertex figure	10 (5/3.4.3.4) 10 (3.4.3/2.4/3)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {11-4{\sqrt {5}}}}{2}}\approx 0.7168905234$
Volume	$0$
Height	Stellated decagram atop pseudo decagram: ${\sqrt {\frac {5-{\sqrt {5}}}{10}}}\approx 0.8506508084$
Related polytopes
Conjugate	Pentagonal cupolaic blend
Convex hull	Decagonal antipodium
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	I2(10)×I, order 12
Convex	No
Nature	Tame

The pentagrammic cupolaic blend is a segmentohedron. It consists of 10 triangles, 10 squares, and 2 pentagrams. It is a cupolaic blend of two pentagrammic cupolas sharing a decagrammic face which blends out.

It is a segmentohedron as a stellated decagram atop pseudo decagram.

It is isomorphic to the pentagonal gyrobicupola.

External links

• Klitzing, Richard. Cupolaic Blends.