TRUNCATED TETRAHEDRON


The 'truncated tetrahedron' is an Archimedean solid. It has 4 regular hexagonal faces, 4 regular triangular faces, 12 vertices and 18 edges.

Contents
Area and volume
Cartesian coordinates
See also
References
External links

Area and volume


The area ''A'' and the volume ''V'' of a truncated tetrahedron of edge length ''a'' are:
:A = 7sqrt{3}a^2 pprox 12.1243557a^2
:V = rac{23}{12}sqrt{2}a^3 pprox 2.71057599a^3

Cartesian coordinates


The set of vertex permutations (±1,±1,±3) with an odd number of minus signs forms a complimentary truncated tetrahedron, and combined they form a uniform compound polyhedron.

Cartesian coordinates for the 12 vertices of a truncated tetrahedron centered at the origin, with edge length √8, are all permutations of (±1,±1,±3) with an even number of minus signs:

★ (+3,+1,+1), (+1,+3,+1), (+1,+1,+3)

★ (−3,−1,+1), (−1,−3,+1), (−1,−1,+3)

★ (−3,+1,−1), (−1,+3,−1), (−1,+1,−3)

★ (+3,−1,−1), (+1,−3,−1), (+1,−1,−3)

See also



★ octahedron

★ tetrahedron

References



★ The Geometrical Foundation of Natural Structure: A Source Book of Design, , Robert, Williams, Dover Publications, Inc, 1979, ISBN 0-486-23729-X (Section 3-9)

External links



★

★ The Uniform Polyhedra

★ Virtual Reality Polyhedra The Encyclopedia of Polyhedra

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