Compound of dodecahedron and icosahedron

First stellation of icosidodecahedron
Type	Dual compound
Stellation core	icosidodecahedron
Convex hull	Rhombic triacontahedron
Index	W47
Polyhedra	1 icosahedron 1 dodecahedron
Faces	20 triangles 12 pentagons
Edges	60
Vertices	32
Symmetry group	icosahedral (Ih)

A rendering of a wooden dodecahedron-icosahedron compound.

In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound.

As a compound

It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual.

It has icosahedral symmetry (I_h) and the same vertex arrangement as a rhombic triacontahedron.

As a stellation

This polyhedron is the first stellation of the icosidodecahedron, and given as Wenninger model index 47.

The stellation facets for construction are:

References

• Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9. 

External links

Dodecahedron-Icosahedron Compound, from Wolfram MathWorld

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Polyhedral stellation Polyhedral compounds Polyhedron stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? Tricholoma sulphureum Karen Ziemba Look at other dictionaries: Compound of small stellated dodecahedron and great dodecahedron — The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is interior to its dual, the small stellated dodecahedron …   Wikipedia Polyhedral compound — A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three dimensional analogs of polygonal compounds such as the hexagram. Neighbouring vertices of a compound can be… …   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 Compound of great icosahedron and great stellated dodecahedron — 15th stellation of icosidodecahedron Type stellation and compound Convex hull Rhombic triacontahedron …   Wikipedia Compound of five tetrahedra — Type Regular compound Index UC5, W24 Elements (As a compound) 5 tetrahedra: F = 20 …   Wikipedia Compound of ten tetrahedra — Type regular compound Index UC6, W25 Elements (As a compound) 10 tetrahedra: F = 40, E = 60, V = 20 …   Wikipedia Compound of five octahedra — Type Regular compound Index UC17, W23 Elements (As a compound) 5 octahedra: F = 40, E = 60, V = 30 …   Wikipedia Icosahedron — In geometry, an icosahedron (Greek: eikosaedron , from eikosi twenty + hedron seat; IPA|/ˌaɪ.kəʊ.sə.ˈhi.dɹən/; plural: drons, dra IPA|/ dɹə/) isany polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral… …   Wikipedia Final stellation of the icosahedron — Two symmetric orthographic projections Symmetry group icosahedra …   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 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”