Octahemioctahedron

Octahemioctahedron
Type	Uniform star polyhedron
Elements	F = 12, E = 24 V = 12 (χ = 0)
Faces by sides	8{3}+4{6}
Wythoff symbol	3/2 3 | 3
Symmetry group	Oh, [4,3], *432 Td, [3,3], *332
Index references	U03, C37, W68
3.6.3/2.6 (Vertex figure)	Octahemioctacron (dual polyhedron)

In geometry, the octahemioctahedron is a nonconvex uniform polyhedron, indexed as U₃. Its vertex figure is a crossed quadrilateral.

It is one of nine hemipolyhedra with 4 hexagonal faces passing through the model center.

Related polyhedra

It shares the vertex arrangement and edge arrangement with the cuboctahedron (having the triangular faces in common), and with the cubohemioctahedron (having the hexagonal faces in common).

Cuboctahedron

Cubohemioctahedron

Octahemioctahedron

By construction it has tetrahedral symmetry (T_d), like the cantellated tetrahedron construction for the cuboctahedron, , with alternate triangles with inverted orientations. Without alternating triangles, it has octahedral symmetry (O_h).

Orientability

It is the only hemipolyhedron that is orientable, and the only uniform polyhedron with an Euler characteristic of zero (a topological torus).

The topological net of faces can be arranged as a rhombus divided into 8 triangles and 4 hexagons. All vertex angle defects are zero.

The net represents a region of the trihexagonal tiling plane, with Wythoff symbol 3 3 | 3 and Coxeter-Dynkin diagram .

See also

• Compound of five octahemioctahedra

External links

• Eric W. Weisstein, Octahemioctahedron (Uniform polyhedron) at MathWorld.
• Uniform polyhedra and duals

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Toroidal polyhedra Polyhedron stubs Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? References regarding the United States Republican Party Crambe abyssinica Look at other dictionaries: Octahemioctacron — Type Star polyhedron Elements F = 12, E = 24 V = 12 (χ = 0) Symmetry group Oh, [4,3], *432 Td, [3,3], *332 …   Wikipedia Cuboctahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 14, E = 24, V = 12 (χ = 2) Faces by sides 8{3}+6{4} …   Wikipedia Cubohemioctahedron — Type Uniform star polyhedron Elements F = 10, E = 24 V = 12 (χ = −2) Faces by sides 6{4}+4{6} Wythoff symbol 4/3 …   Wikipedia Hemipolyhedron — In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These hemi faces lie parallel to the faces of some other symmetrical polyhedron, and their count is half the number of faces of that other… …   Wikipedia Liste Des Polyèdres Uniformes — Les polyèdres uniformes et les pavages forment un groupe bien étudié. Ils sont listés ici pour une comparaison rapide de leurs propriétés et de leurs noms de schéma variés ainsi que de leurs symboles. Cette liste inclut : tous les 75… …   Wikipédia en Français Liste des polyedres uniformes — Liste des polyèdres uniformes Les polyèdres uniformes et les pavages forment un groupe bien étudié. Ils sont listés ici pour une comparaison rapide de leurs propriétés et de leurs noms de schéma variés ainsi que de leurs symboles. Cette liste… …   Wikipédia en Français Liste des polyèdres uniformes — Cette liste recense les polyèdres uniformes, ainsi que certaines de leurs propriétés. Sommaire 1 Méthodologie 2 Table des polyèdres 2.1 Formes convexes (3 faces/sommet) …   Wikipédia en Français Uniform star polyhedron — A display of uniform polyhedra at the Science Museum in London …   Wikipedia List of mathematics articles (O) — NOTOC O O minimal theory O Nan group O(n) Obelus Oberwolfach Prize Object of the mind Object theory Oblate spheroid Oblate spheroidal coordinates Oblique projection Oblique reflection Observability Observability Gramian Observable subgroup… …   Wikipedia Dodecadodecahedron — Type Uniform star polyhedron Elements F = 24, E = 60 V = 30 (χ = −6) Faces by sides 12{5}+12{5/2} Wythoff symbol …   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”