# G3

G3 Rank3
TypeAcrohedron
SpaceSpherical
Notation
Stewart notationG3
Elements
Faces1 + 6 triangles, 3 pentagons, 3 squares
Edges3 + 3 + 3 + 3 + 6 + 6 = 24
Vertices1 + 3 + 3 + 6 = 13
Abstract & topological properties
Flag count96
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×I, order 6
ConvexNo
NatureTame

G3 is a non-convex regular faced polyhedron. It was the smallest known 5-4-3 acrohedron until the discovery of m*, which has one face fewer. It was named by Bonnie Stewart in Adventures Among the Toroids, although Stewart was not searching for acrohedra in particular.

## Vertex coordinates

The vertex coordinates of a G3 with unit edge length are given by:

• $\left(\pm\frac{1+\sqrt5}{4},\,\pm\frac{1+\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),$ • $\left(\pm\frac12,\,0,\,\frac{3+\sqrt5}{4}\right),$ • $\left(0,\,\pm\frac{3+\sqrt5}{4},\,\frac12\right),$ • $\left(\frac{3+\sqrt5}{4},\,\pm\frac12,\,0\right),$ • $\left(\frac{\sqrt5-1}{4},\,\pm\frac12,\,0\right),$ • $\left(-\frac12,\,0,\,\frac{\sqrt5-1}{4}\right).$ 