Small triambic icosahedron


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 intersected hexagonal faces are divided and new edges created, this figure becomes the triakis icosahedron. The descriptive name "triakis icosahedron" represents a topological construction starting with an icosahedron and adding short triangular pyramids. With the proper pyramid height this figure becomes a Catalan solid by the same name and the dual of the truncated dodecahedron).

The nonconvex uniform polyhedra great stellated dodecahedron and great dodecahedron, as viewed as surface topologies, can also be constructed as icosahedron with pyramids, the first with much tall pyramids, and the second with inverted ones.

As a stellation

This figure is also the first stellation of the icosahedron, and given as Wenninger model index 26.

This stellation is a popular subject for construction in modular origami, often made of thirty Sonobe units.

References

* (p. 46, Model "W"26, triakis icosahedron)
* (pp. 42–46, dual to uniform polyhedron "W"70)
*Citation | last1=Coxeter | first1=Harold Scott MacDonald | author1-link=Harold Scott MacDonald Coxeter | last2=Du Val | first2=P. | last3=Flather | first3=H. T. | last4=Petrie | first4=J. F. | title=The fifty-nine icosahedra | publisher=Tarquin | edition=3rd | isbn=978-1-899618-32-3 | id=MathSciNet | id = 676126 | year=1999 (1st Edn University of Toronto (1938))

External links

*


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Great triambic icosahedron — Medial triambic icosahedron Types …   Wikipedia

  • Final stellation of the icosahedron — Two symmetric orthographic projections Symmetry group icosahedra …   Wikipedia

  • Compound of five octahedra — Type Regular compound Index UC17, W23 Elements (As a compound) 5 octahedra: F = 40, E = 60, V = 30 …   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

  • 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

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Petit icosidodecaedre ditrigonal — Petit icosidodécaèdre ditrigonal Petit icosidodécaèdre ditrigonal Type Polyèdre uniforme Éléments F=32, A=60, S=20 (χ= 8) Faces par cotés 20{3}+12{5/ …   Wikipédia en Français

  • Petit icosidodécaèdre ditrigonal — Type Polyèdre uniforme Éléments F=32, A=60, S=20 (χ= 8) Faces par côtés 20{3}+12{5/2} …   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


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.