Blend of 2 pentagrammic pyramids

Blend of 2 pentagrammic pyramids
(OFF file)
Rank	3
Type	Orbiform
Space	Spherical
Notation
Bowers style acronym	Gifbah
Elements
Faces	2+4 triangles, 2 pentagrams
Edges	2+4+4+4
Vertices	2+2+4
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{8}} \approx 0.58779$
Number of external pieces	28
Level of complexity	53
Related polytopes
Conjugate	Blend of 2 pentagonal pyramids
Abstract & topological properties
Flag count	56
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	K2×I, order 4
Convex	No
Nature	Tame

The blend of 2 pentagrammic pyramids, or gifbah, is an orbiform polyhedron. It consists of 6 triangles and 2 pentagrams. It is a faceting of the great icosahedron and thus also of the small stellated dodecahedron. As its name suggests, it can be formed by blending two pentagrammic pyramids together such that they share an edge and the two triangles adjacent to that edge.

It appears as a cell of the great stellated dodecahedral extended double antiprism.

Vertex coordinates

The vertices of a blend of 2 pentagrammic pyramids of edge length 1 are:

• $\left(\pm\frac{1-\sqrt{5}}{4},\,0,\,\pm\frac{1}{2}\right),$
• $\left(\pm\frac{1}{2},\,-\frac{1-\sqrt{5}}{4},\,0\right),$
• $\left(0,\,\frac{1}{2},\,\pm\frac{1-\sqrt{5}}{4}\right).$

Gallery

External links

• Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#16 under sissid).