G3

G3
(3D model) (OFF file)
Rank	3
Type	Acrohedron
Notation
Stewart notation	G3
Elements
Faces	1 + 6 triangles, 3 pentagons, 3 squares
Edges	3 + 3 + 3 + 3 + 6 + 6 = 24
Vertices	1 + 3 + 3 + 6 = 13
Abstract & topological properties
Flag count	96
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	A2×I, order 6
Convex	No
Nature	Tame

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:

• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,{\frac {1+{\sqrt {5}}}{4}}\right),$
• $\left(\pm {\frac {1}{2}},\,0,\,{\frac {3+{\sqrt {5}}}{4}}\right),$
• $\left(0,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,{\frac {1}{2}}\right),$
• $\left({\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,0\right),$
• $\left({\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1}{2}},\,0\right),$
• $\left(-{\frac {1}{2}},\,0,\,{\frac {{\sqrt {5}}-1}{4}}\right).$

External links

• Jim McNeill. "The Stewart G3 and its relations"
• Alex Doskey. "Stewart G₃"
• McCooey, David. "Stewart's G3"