Great triambic icosahedron

	Great triambic icosahedron	Medial triambic icosahedron
Types	Dual uniform polyhedra
Symmetry group	Ih
Name	Great triambic icosahedron	Medial triambic icosahedron
Index references	DU47, W34, 30/59	DU41, W34, 30/59
Elements	F = 20, E = 60 V = 32 (χ = -8)	F = 20, E = 60 V = 24 (χ = -16)
Isohedral faces
Duals	Great ditrigonal icosidodecahedron	Ditrigonal dodecadodecahedron
Stellation
Icosahedron: W34
Stellation diagram

In geometry, the great triambic icosahedron and medial triambic icosahedron are visually identical dual uniform polyhedra. The exterior surface also represents the De₁f₁ stellation of the icosahedron. The only way to differentiate these two polyhedra is to mark which intersections between edges are true vertices and which are not. In the above images, true vertices are marked by gold spheres.

The 12 vertices of the convex hull matches the vertex arrangement of an icosahedron.

Great triambic icosahedron

The great triambic icosahedron is the dual of the great ditrigonal icosidodecahedron, U47. It has 20 inverted-hexagonal faces, shaped like a three-bladed propeller. It has 32 vertices: 12 exterior points, and 20 hidden inside. It has 60 edges.

Medial triambic icosahedron

The medial triambic icosahedron is the dual of the ditrigonal dodecadodecahedron, U41. It has 20 faces, each being simple concave isogonal hexagons. It has 24 vertices: 12 exterior points, and 12 hidden inside. It has 60 edges.

Unlike the great triambic icosahedron, the medial triambic icosahedron is topologically a regular polyhedron of index two.^[1] By distorting the triambi into regular hexagons, one obtains the hyperbolic order-5 hexagonal tiling:

As a stellation

It is Wenninger's 34th model in his 9th stellation of the icosahedron

See also

• Triakis icosahedron
• Small triambic icosahedron

References

• Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9. 
• Wenninger, Magnus (1983). Dual Models. Cambridge University Press. ISBN 978-0-521-54325-5. MR730208. 

1. ^ The Regular Polyhedra (of index two), David A. Richter

External links

• Weisstein, Eric W., "Great triambic icosahedron" from MathWorld.
• Weisstein, Eric W., "Medial triambic icosahedron" from MathWorld.
• gratrix.net Uniform polyhedra and duals
• bulatov.org Medial triambic icosahedron Great triambic icosahedron

Notable stellations of the icosahedron
Regular	Uniform duals		Regular compounds			Regular star	Others
Icosahedron	Small triambic icosahedron	Great triambic icosahedron	Compound of five octahedra	Compound of five tetrahedra	Compound of ten tetrahedra	Great icosahedron	Excavated dodecahedron	Final stellation
The stellation process on the icosahedron creates a number of related polyhedra and compounds with icosahedral symmetry.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Polyhedra Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР Medial striate artery Medial vestibulospinal tract Look at other dictionaries: Small triambic icosahedron — In geometry, the small triambic icosahedron is the dual to the uniform small ditrigonal icosidodecahedron. It is composed of 20 intersecting isogonal hexagon faces. It has 60 edges and 32 vertices, and Euler characteristic of −8.If the… …   Wikipedia Final stellation of the icosahedron — Two symmetric orthographic projections Symmetry group icosahedra …   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 Grand Icosidodécaèdre Ditrigonal — Type Polyèdre uniforme Éléments F=32, A=60, S=20 (χ= 8) Faces par cotés 20{3}+12{5} …   Wikipédia en Français Grand icosidodecaedre ditrigonal — Grand icosidodécaèdre ditrigonal Grand icosidodécaèdre ditrigonal Type Polyèdre uniforme Éléments F=32, A=60, S=20 (χ= 8) Faces par cotés 20{3}+12{5} …   Wikipédia en Français Grand icosidodécaèdre ditrigonal — Type Polyèdre uniforme Éléments F=32, A=60, S=20 (χ= 8) Faces par côtés 20{3}+12{5} Configuration de …   Wikipédia en Français Ditrigonal dodecadodecahedron — Type Uniform star polyhedron Elements F = 24, E = 60 V = 20 (χ = −16) Faces by sides 12{5}+12{5/2} Wy …   Wikipedia List of Tron characters — This article covers notable characters of Tron franchise, including all of its various cinematic, literary, video game adaptations and sequels. Contents 1 Development 2 Tron 2.1 Bit 2.2 Lora Baines …   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”