The 'truncated tetrahedron' is an
Archimedean solid. It has 4 regular
hexagonal faces, 4 regular
triangular faces, 12 vertices and 18 edges.
Area and volume
The area ''A'' and the
volume ''V'' of a truncated tetrahedron of edge length ''a'' are:
:
:
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.
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
العربية
中国
Français
Deutsch
Ελληνική
हिन्दी
Italiano
日本語
Português
Русский
Español
