About: Tetrahedrally diminished dodecahedron

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In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals). A canonical form exists with two edge lengths at 0.849 : 1.057, assuming that the radius of the midsphere is 1. The kites remain isosceles. Topologically, the triangles are always equilateral, while the quadrilaterals are irregular, although the two adjacent edges that meet at the vertices of a tetrahedron are equal.

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rdfs:label	Tetrahedrally diminished dodecahedron (en)
rdfs:comment	In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals). A canonical form exists with two edge lengths at 0.849 : 1.057, assuming that the radius of the midsphere is 1. The kites remain isosceles. Topologically, the triangles are always equilateral, while the quadrilaterals are irregular, although the two adjacent edges that meet at the vertices of a tetrahedron are equal. (en)
foaf:depiction
dcterms:subject	Polyhedra
Wikipage page ID	40710756 (xsd:integer)
Wikipage revision ID	1092444989 (xsd:integer)
Link from a Wikipage to another Wikipage	Pseudoicosahedron Pyritohedron Quadrilateral Regular dodecahedron Regular icosahedron VRML Vertex configuration Pentagonal antiprism Conway polyhedron notation Midsphere Equilateral triangle Geometry George W. Hart Convex polytope Dual polyhedron Polyhedra Tetrahedron Vertex figure Hexadecahedron Trapezoid Triangle Dodecahedron Kite (geometry) Schlegel diagram Uniform honeycombs in hyperbolic space Self-dual polyhedron Tetrahedral symmetry List of spherical symmetry groups Stellation Partially diminished icosahedral honeycomb Pyritohedral symmetry Diminishment (geometry)
Link from a Wikipage to an external page	http://www.georgehart.com/virtual-polyhedra/vrml/tetrahedrally_stellated_icosahedron.wrl http://www.georgehart.com/virtual-polyhedra/vrml/tetrahedrally_truncated_dodecahedron.wrl http://www.mi.sanu.ac.rs/vismath/zefiro2008/__generation_of_icosahedron_by_5tetrahedra.htm http://www.ac-noumea.nc/maths/polyhedr/tetra_di_.htm
sameAs	Tetrahedrally diminished dodecahedron Tetrahedrally diminished dodecahedron Tetrahedrally diminished dodecahedron
dbp:wikiPageUsesTemplate	dbt:Efn dbt:Math dbt:Mvar dbt:Notelist dbt:Reflist dbt:Short_description dbt:Polyhedra dbt:Polyhedron_navigator
thumbnail	wiki-commons:Special:FilePath/Tetrahedral_self-dual_hexadecahedron.png?width=300
has abstract	In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals). A canonical form exists with two edge lengths at 0.849 : 1.057, assuming that the radius of the midsphere is 1. The kites remain isosceles. It has chiral tetrahedral symmetry, and so its geometry can be constructed from pyritohedral symmetry of the pseudoicosahedron with 4 faces stellated, or from the pyritohedron, with 4 vertices diminished. Within its tetrahedral symmetry, it has geometric varied proportions. By Dorman Luke dual construction, a unique geometric proportion can be defined. The kite faces have edges of length ratio ~ 1:0.633. Topologically, the triangles are always equilateral, while the quadrilaterals are irregular, although the two adjacent edges that meet at the vertices of a tetrahedron are equal. As a self-dual hexadecahedron, it is one of 302404 forms, 1476 with at least order 2 symmetry, and the only one with tetrahedral symmetry. As a diminished regular dodecahedron, with 4 vertices removed, the quadrilaterals faces are trapezoids. As a stellation of the regular icosahedron it is one of 32 stellations defined with tetrahedral symmetry. It has kite faces. In Conway polyhedron notation, it can represented as pT, applying George W. Hart's propeller operator to a regular tetrahedron. (en)
prov:wasDerivedFrom	wikipedia-en:Tetrahedrally_diminished_dodecahedron?oldid=1092444989&ns=0
page length (characters) of wiki page	4978 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tetrahedrally_diminished_dodecahedron
is Link from a Wikipage to another Wikipage of	Tetrated dodecahedron Hexadecahedron Truncation (geometry) Diminished trapezohedron Icosahedral honeycomb Uniform honeycombs in hyperbolic space Polytope Propello tetrahedron Tetrahedrally stellated icosahedron Tetrahedrally truncated dodecahedron
is Wikipage redirect of	Propello tetrahedron Tetrahedrally stellated icosahedron Tetrahedrally truncated dodecahedron
is foaf:primaryTopic of	wikipedia-en:Tetrahedrally_diminished_dodecahedron

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