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- Tetrahemihexahedron abstract "In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 6 vertices and 12 edges, and 7 faces: 4 triangular and 3 square. Its vertex figure is a crossed quadrilateral. Its Coxeter-Dynkin diagram is File:CDel node 1.pngFile:CDel 3x.pngFile:CDel rat.pngFile:CDel d2.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.png (although this is a double covering of the tetrahemihexahedron).It is the only non-prismatic uniform polyhedron with an odd number of faces. Its Wythoff symbol is 3/2 3 | 2, but actually that represents a double covering of the tetrahemihexahedron with 8 triangles and 6 squares, paired and coinciding in space. (It can more intuitively be seen as two coinciding tetrahemihexahedra.)It is a hemipolyhedron. The "hemi" part of the name means some of the faces form a group with half as many members as some regular polyhedron—here, three square faces form a group with half as many faces as the regular hexahedron, better known as the cube—hence hemihexahedron. Hemi faces are also oriented in the same direction as the regular polyhedron's faces. The three square faces of the tetrahemihexahedron are, like the three facial orientations of the cube, mutually perpendicular.The "half-as-many" characteristic also means that hemi faces must pass through the center of the polyhedron, where they all intersect each other. Visually, each square is divided into four right triangles, with two visible from each side.It is the three-dimensional demicross polytope.".
- Tetrahemihexahedron thumbnail RomanSurfaceTopView.PNG?width=300.
- Tetrahemihexahedron wikiPageExternalLink summary.
- Tetrahemihexahedron wikiPageExternalLink rptwo.htm.
- Tetrahemihexahedron wikiPageExternalLink Stella.php.
- Tetrahemihexahedron wikiPageExternalLink Tetrahemi.php.
- Tetrahemihexahedron wikiPageID "2851834".
- Tetrahemihexahedron wikiPageRevisionID "606317116".
- Tetrahemihexahedron hasPhotoCollection Tetrahemihexahedron.
- Tetrahemihexahedron title "Tetrahemihexacron".
- Tetrahemihexahedron title "Tetrahemihexahedron".
- Tetrahemihexahedron title "Uniform polyhedron".
- Tetrahemihexahedron urlname "Tetrahemihexacron".
- Tetrahemihexahedron urlname "Tetrahemihexahedron".
- Tetrahemihexahedron urlname "UniformPolyhedron".
- Tetrahemihexahedron subject Category:Projective_polyhedra.
- Tetrahemihexahedron subject Category:Uniform_polyhedra.
- Tetrahemihexahedron comment "In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 6 vertices and 12 edges, and 7 faces: 4 triangular and 3 square. Its vertex figure is a crossed quadrilateral.".
- Tetrahemihexahedron label "Tetrahemihexahedron".
- Tetrahemihexahedron label "Tétrahémihexaèdre".
- Tetrahemihexahedron label "四面半六面体".
- Tetrahemihexahedron label "四面半六面體".
- Tetrahemihexahedron sameAs Tétrahémihexaèdre.
- Tetrahemihexahedron sameAs 四面半六面体.
- Tetrahemihexahedron sameAs 사면반육면체.
- Tetrahemihexahedron sameAs m.086wbh.
- Tetrahemihexahedron sameAs Q3100395.
- Tetrahemihexahedron sameAs Q3100395.
- Tetrahemihexahedron wasDerivedFrom Tetrahemihexahedron?oldid=606317116.
- Tetrahemihexahedron depiction RomanSurfaceTopView.PNG.
- Tetrahemihexahedron isPrimaryTopicOf Tetrahemihexahedron.
.It%20is%20the%20only%20non-prismatic%20uniform%20polyhedron%20with%20an%20odd%20number%20of%20faces.%20Its%20Wythoff%20symbol%20is%203%2F2%203%20%7C%202%2C%20but%20actually%20that%20represents%20a%20double%20covering%20of%20the%20tetrahemihexahedron%20with%208%20triangles%20and%206%20squares%2C%20paired%20and%20coinciding%20in%20space.%20(It%20can%20more%20intuitively%20be%20seen%20as%20two%20coinciding%20tetrahemihexahedra.)It%20is%20a%20hemipolyhedron.%20The%20%22hemi%22%20part%20of%20the%20name%20means%20some%20of%20the%20faces%20form%20a%20group%20with%20half%20as%20many%20members%20as%20some%20regular%20polyhedron%E2%80%94here%2C%20three%20square%20faces%20form%20a%20group%20with%20half%20as%20many%20faces%20as%20the%20regular%20hexahedron%2C%20better%20known%20as%20the%20cube%E2%80%94hence%20hemihexahedron.%20Hemi%20faces%20are%20also%20oriented%20in%20the%20same%20direction%20as%20the%20regular%20polyhedron's%20faces.%20The%20three%20square%20faces%20of%20the%20tetrahemihexahedron%20are%2C%20like%20the%20three%20facial%20orientations%20of%20the%20cube%2C%20mutually%20perpendicular.The%20%22half-as-many%22%20characteristic%20also%20means%20that%20hemi%20faces%20must%20pass%20through%20the%20center%20of%20the%20polyhedron%2C%20where%20they%20all%20intersect%20each%20other.%20Visually%2C%20each%20square%20is%20divided%20into%20four%20right%20triangles%2C%20with%20two%20visible%20from%20each%20side.It%20is%20the%20three-dimensional%20demicross%20polytope.%22%40en){kind=link}
