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Rectified truncated dodecahedron

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Rectified truncated dodecahedron
Faces92:
20 equilateral triangles
60 isosceles triangles
12 decagons
Edges180
Vertices90
Schläfli symbolrt{5,3}
Conway notationatD
Symmetry groupIh, [5,3], (*532), order 120
Rotation groupI, [5,3]+, (532), order 60
Dual polyhedronJoined truncated dodecahedron
Propertiesconvex
Net

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

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.

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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

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References

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  • 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-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5
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