Triaprism
In geometry of 6 dimensions or higher, a triaprism (or triprism) is a polytope resulting from the Cartesian product of three polytopes, each of two dimensions or higher. The Cartesian product of an a-polytope, a b-polytope, and a c-polytope is an (a+b+c)-polytope, where a, b and c are 2-polytopes (polygon) or higher.
The term triaprism is coined by George Olshevsky, shortened from triple prism, similar to duoprism for the product of two polytopes. Conway proposed a similar name proprism for product prism, thus applying to any number of products.
The lowest dimensional triaprisms exist in 6-dimensional space as 6-polytopes being the Cartesian product of three polygons in 2-dimensional Euclidean space.
The smallest is a 3-3-3 triaprism or (triangle-triangle-triangle-triaprism), being the product of three triangles. It has 5-faces (3-3 duoprism prisms), 36 4-faces (9 3-3 duoprisms, 27 3-4 duoprism), 81 cells (27 cubes, 54 triangular prisms), 108 faces (81 squares, 27 triangles), 81 edges, and 27 vertices.[1]
See also
- Uniform 6-polytope#Uniform_prismatic_families
- 7-polytope#Uniform_triaprismatic_forms
- 8-polytope#Uniform_triaprismatic_forms
Notes
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26)
External links
- Olshevsky, George, Duoprism and Triaprism at Glossary for Hyperspace.
- Olshevsky, George, Cartesian product at Glossary for Hyperspace.