truncated tetrahedron

English

A truncated tetrahedron

Noun

truncated tetrahedron (plural truncated tetrahedra or truncated tetrahedrons)

1. (geometry) A convex polyhedron, with four triangular and four hexagonal faces, that is an Archimedean solid and can be constructed by truncating a regular tetrahedron at each vertex by one-third the length of each adjoining edge.
   • 1968, Cindy Marriott, A Critical Analysis of Israeli Architecture, 1948-1967: A Study in Cultural Conflict‎^[1], page 63:

     The space of the El Al pyramid is created essentially by the packing of truncated tetrahedrons.

   • 1976, Anthony Pugh, An Introduction to Tensegrity‎^[2], page 35:

     The tendons now form the edges of a slightly distorted truncated tetrahedron.

   • 2000, Angel Vegas, Cations in Inorganic Solids: Crystallography Reviews, volume 7, number 3, page 248:

     This ideal net gives rise to the formation of B₁₂ truncated tetrahedra, where the A cations are lodged.

   • 2009, Xiaotian Lin, Miao Jin, Feng Luo, Xiangfen David Gu, Discrete Curvature Flows for Surfaces and 3-Manifolds, Frank Nielsen (editor), Emerging Trends in Visual Computing: LIX Fall Colloquium, ETVC 2008, page 69,

     Once the edge lengths of the tetrahedral mesh have been obtained, we can realize it in the hyperbolic space ℍ³ First, we introduce how to construct a single truncated tetrahedron; then we explain how to glue multiple truncated tetrahedra by hyperbolic rigid motion.

   • 2010, K.M. Kosuda, J. M. Bingham, K. L. Wustholz, R. P. Van Dyne, 9: Nanostructures and Surface-Enhanced Raman Spectroscopy, Gary P. Wiederrecht (efitor), Handbook of Nanoscale Optics and Electronics, page 318,

     Without any further modification, the shapes of the nanoparticles fabricated by NSL are truncated tetrahedrons. However, by thermal annealing the truncated tetrahedrons are transformed into hemispheres.