Rectified truncated dodecahedron

The rectified truncated dodecahedron is a polyhedron, constructed as a rectified truncated dodecahedron. It has 92 faces: 20 equilateral triangles, 60 isosceles triangles, and 12 decagons.

Rectified truncated dodecahedron
Schläfli symbol	rt{5,3}
Conway notation	atD
Faces	92: 20 {3} 60 { }∨( ) 12 {10}
Edges	180
Vertices	90
Symmetry group	Ih, [5,3], (*532) order 120
Rotation group	I, [5,3]^+, (532), order 60
Dual polyhedron	Joined truncated dodecahedron
Properties	convex
Net

Topologically, the triangles corresponding to the dodecahedrons's vertices are always equilateral, although the decagons, while having equal edge lengths, do not have the same edge lengths with the equilateral triangles, having different but alternating angles, causing the other triangles to be isosceles instead.

Related polyhedra

The rectified truncated dodecahedron can be seen in sequence of rectification and truncation operations from the dodecahedron. Further truncation, and alternation operations creates two more polyhedra:

Name	Truncated dodecahedron	Rectified truncated dodecahedron	Truncated rectified truncated dodecahedron	Snub rectified truncated dodecahedron
Coxeter	tD	rtD	trtD	srtD
Conway		atD	btD	stD
Image

See also

• Rectified truncated tetrahedron
• Rectified truncated octahedron
• Rectified truncated cube
• Rectified truncated icosahedron

References

• Coxeter Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (pp. 145–154 Chapter 8: Truncation)
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5

External links

• George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input