Disdyakis dodecahedron

Disdyakis dodecahedron
Click on picture for large version Spinning version
Type	Catalan
Face polygon	scalene triangle
Faces	48
Edges	72
Vertices	26 = 6 + 8 + 12
Face configuration	V4.6.8
Symmetry group	Oh, [4,3], *432
Dihedral angle	155° 4' 56" $\arccos ( -\frac{71 + 12\sqrt{2}}{97} )$
Dual polyhedron	truncated cuboctahedron
Properties	convex, face-transitive
Net

In geometry, a disdyakis dodecahedron, or hexakis octahedron, is a Catalan solid and the dual to the Archimedean truncated cuboctahedron. As such it is face-transitive but with irregular face polygons. It looks a bit like an inflated rhombic dodecahedron—if one replaces each face of the rhombic dodecahedron with a single vertex and four triangles in a regular fashion one ends up with a disdyakis dodecahedron. More formally, the disdyakis dodecahedron is the Kleetope of the rhombic dodecahedron.

Symmetry

It has O_h octahedral symmetry. Its collective edges represent the reflection planes of the symmetry.

Dimensions

If its smallest edges have length 1, its surface area is $\frac{6}{7}\sqrt{783+436\sqrt{2}}$ and its volume is $\frac{1}{7}\sqrt{3(2194+1513\sqrt{2})}$.

See also

• Disdyakis triacontahedron
• Bisected hexagonal tiling
• Great rhombihexacron—A uniform dual polyhedron with the same surface topology

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 285, kisRhombic dodecahedron )

External links

• Eric W. Weisstein, Disdyakis dodecahedron (Catalan solid) at MathWorld.
• Disdyakis Dodecahedron (Hexakis Octahedron) Interactive Polyhedron Model

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Catalan solids Polyhedron stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Kipple Deltoidal hexecontahedron Look at other dictionaries: Disdyakis triacontahedron — Click on picture for large version spinning version Type Catalan Face polygon scalene triangle Faces 120 Edges …   Wikipedia Dodecahedron — Regular Dodecahedron (Click here for rotating model) Type Platonic solid Elements F = 12, E = 30 V = 20 (χ = 2) Faces by sides 12{5} …   Wikipedia Snub dodecahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 92, E = 150, V = 60 (χ = 2) Faces by sides (20+60 …   Wikipedia Truncated great dodecahedron — Type Uniform star polyhedron Elements F = 24, E = 90 V = 60 (χ = −6) Faces by sides 12{5/2}+12{10} Wythof …   Wikipedia Truncated cuboctahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 26, E = 72, V = 48 (χ = 2) Faces by sides …   Wikipedia Tetrakis hexahedron — (Click here for rotating model) Type Catalan solid Face type isosceles triangle Faces 24 Edges 36 Vert …   Wikipedia Truncated icosidodecahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 62, E = 180, V = 120 (χ = 2) Faces by sides …   Wikipedia Octahedral symmetry — The cube is the most common shape with octahedral symmetry A regular octahedron has 24 rotational (or orientation preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation. A cube has… …   Wikipedia Catalanische Körper — Ein catalanischer Körper oder auch dual archimedischer Körper ist ein Körper, der sich zu einem archimedischen Körper dual verhält. So ist zum Beispiel das Rhombendodekaeder dual zum Kuboktaeder. Benannt sind catalanische Körper nach dem… …   Deutsch Wikipedia Dual-Archimedischer Körper — Ein catalanischer Körper oder auch dual archimedischer Körper ist ein Körper, der sich zu einem archimedischen Körper dual verhält. So ist zum Beispiel das Rhombendodekaeder dual zum Kuboktaeder. Benannt sind catalanische Körper nach dem… …   Deutsch Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”