Deltoidal hexecontahedron

Deltoidal hexecontahedron
Click on picture for large version spinning version
Type	Catalan
Face polygon	kite
Faces	60
Edges	120
Vertices	62 = 12 + 20 + 30
Face configuration	V3.4.5.4
Symmetry group	Ih, [5,3], *532
Dihedral angle	154° 8'
Properties	convex, face-transitive
rhombicosidodecahedron (dual polyhedron)	Net

In geometry, a deltoidal hexecontahedron (also sometimes called a trapezoidal hexecontahedron, a strombic hexecontahedron, or a tetragonal hexacontahedron) is a catalan solid which looks a bit like either an overinflated dodecahedron or icosahedron. It is sometimes also called the trapezoidal hexecontahedron or strombic hexecontahedron. Its dual polyhedron is the rhombicosidodecahedron.

The 60 faces are deltoids or kites (not trapezoidal). The short and long edges of each kite are in the ratio 1.00:1.54.

It is the only Archimedean dual which does not have a Hamiltonian path among its vertices.

See also

• Deltoidal icositetrahedron

References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.  (Section 3-9)
• The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ISBN 978-1-56881-220-5 [1] (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 286, tetragonal hexecontahedron)

External links

• Eric W. Weisstein, DeltoidalHexecontahedron and Hamiltonian path (Catalan solid) at MathWorld.
• Deltoidal Hexecontahedron (Trapezoidal Hexecontrahedron) -- Interactive Polyhedron Model

• Example in real life -- A ball almost 4 meters in diameter, from ripstop nylon, and inflated by the wind. It bounces around on the ground so that kids can play with it at kite festivals.