# Blend of 2 pentagrammic pyramids

Blend of 2 pentagrammic pyramids
Rank3
TypeOrbiform
Notation
Bowers style acronymGifbah
Elements
Faces2+4 triangles, 2 pentagrams
Edges2+4+4+4
Vertices2+2+4
Vertex figures2 crossed isosceles trapezoids, edge lengths 1, 1, 1, (5–1)/2
2 butterflies, edge lengths 1 and (5–1)/2
4 isosceles triangles, edge lengths 1, 1, (5–1)/2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779}$
Volume${\displaystyle {\frac {7-3{\sqrt {5}}}{12}}\approx 0.024316}$
Dihedral angles3-5/2 #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
3-3: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }}$
3-5/2 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Number of external pieces28
Level of complexity53
Related polytopes
ConjugateBlend of 2 pentagonal pyramids
Abstract & topological properties
Flag count56
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
ConvexNo
NatureTame

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:

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