In geometry, the tetrahemihexahedron is a concave uniform polyhedron, indexed as U4. Image File history File links Tetrahemihexahedron. ... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ... A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. ... In plane geometry, a square is a polygon with four equal sides and equal angles. ... The symmetry group of an object (e. ... The tetrahedral rotation group T with fundamental domain; for the triakis tetrahedron, see below, the latter is one full face Chiral and achiral tetrahedral symmetry and pyritohedral symmetry are discrete point symmetries (or equivalently, symmetries on the sphere). ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... In geometry, concavity is a property of certain geometric figures, and in calculus, a property of certain graphs of functions. ... Image File history File links Tetrahemihexahedron_vertfig. ... Geometry (Greek γεωμετÏία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ... A uniform polyhedron is a polyhedron with regular polygons as faces and identical vertices. ...
It contains the same 6 vertices as the regular octahedron. An octahedron (plural: octahedra) is a polyhedron with eight faces. ...
It is the only nonprismatic uniform polyhedron with an odd number of faces.
The "hemi" part of the name means some of the faces pass through the center of the polyhedron, in this case the square faces.
Because the tetrahemihexahedron has the same vertices and edges as the octahedron, one can try to substitute it into the eight different compounds of octahedra just described.
But the tetrahemihexahedron has only tetrahedral symmetry, and as a consequence, it turns out that only two of the results are symmetric.
When a 3-fold axis of a tetrahemihexahedron is aligned to a 3-fold axis of the icosahedral symmetry group, the two ends of the axis are different in that one has a face where the other has an indentation.
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