Pentagonal icositetrahedron

Pentagonal icositetrahedron
Pentagonal icositetrahedron, anticlockwise twistPentagonal icositetrahedron
(Click ccw or cw for rotating models.)
Type Catalan
Conway notation gC
Coxeter diagram
Face polygon
irregular pentagon
Faces 24
Edges 60
Vertices 38 = 6 + 8 + 24
Face configuration V3.3.3.3.4
Dihedral angle 136° 18' 33'
Symmetry group O, 1/2BC3, [4,3]+, 432
Dual polyhedron snub cube
Properties convex, face-transitive, chiral
Pentagonal icositetrahedron
Net
A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira.
3d model of a pentagonal icositetrahedron

In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron[1] is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid.[2][3]

It has two distinct forms, which are mirror images (or "enantiomorphs") of each other.

  1. ^ Conway, Symmetries of things, p.284
  2. ^ "Promorphology of Crystals I".
  3. ^ "Crystal Form, Zones, & Habit". Archived from the original on 2003-08-23.