In 4-dimensional
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the tetrahedral cupola is a
polychoron bounded by one
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
, a parallel
cuboctahedron, connected by 10
triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is ''oblique''. A unif ...
s, and 4
triangular pyramids.
Convex Segmentochora
Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.23 tetrahedron , , cuboctahedron)
Related polytopes
The ''tetrahedral cupola'' can be sliced off from a runcinated 5-cell, on a hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ''ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyper ...
parallel to a tetrahedral cell. The cuboctahedron base passes through the center of the runcinated 5-cell, so the Tetrahedral cupola contains half of the tetrahedron and triangular prism cells of the runcinated 5-cell. The cupola can be seen in A2 and A3 Coxeter plane orthogonal projection of the runcinated 5-cell:
See also
* Tetrahedral pyramid
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is ...
(5-cell)
References
External links
Segmentochora:
4-polytopes
{{Polychora-stub