Hexacon

Not to be confused with Hexagon or Hexasphericon.

Hexacon
(3D model)
Rank	3
Type	Polycon
Measures (radius 1)
Volume	${\frac {4{\sqrt {3}}}{9}}$
Surface area	${\frac {8{\sqrt {3}}}{3}}$
Central density	1
Abstract & topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(G2×A1)/2, order 12
Convex	Yes
Net count	1

The hexacon, also called the parabolicon and the 3-con, is a developable roller in the polycon family. It is the only polycon whose edges are parabolic sections. The sphericon has circular edges and higher degree polycons have hyperbolic edges.

External links

• David Hirsch. "Parabolicon Construction".

Bibliography

• Seaton, Katherine; Hirsch, David (2019). "The polycons: the sphericon (or tetracon) has found its family". arXiv:1901.10677.