# A5''

A5''
Rank3
TypeAcrohedron
Notation
Stewart notationA5''
Elements
Faces
Edges10+10+10+20
Vertices5+5+10
Abstract & topological properties
Flag count200
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH2×A1, order 20
Flag orbits10
ConvexNo

A5'' is a non-convex polyhedron with regular faces. It first appeared in Bonnie Stewart's Adventures Among the Toroids as a component in the construction of a kind of Stewart toroid he calls "accordion polyhedra."

## Vertex coordinates

The vertex coordinates of an A5'', centered at the origin and with unit edge length, are:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}},\,-{\sqrt {\frac {25+11{\sqrt {5}}}{40}}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,0\right)}$,
• ${\displaystyle \left(0,\,{\sqrt {\frac {5+2{\sqrt {5}}}{5}}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,0\right)}$,
• ${\displaystyle \left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,0\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{20}}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)}$,
• ${\displaystyle \left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)}$.

## Related polyhedra

This polyhedron is a special instance of the much larger class of edge-expanded bi-antiprisms, in fact "exo {5} (2,0) EEA".