Truncated tetrahedron - Definition and Overview

Truncated tetrahedron
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Type	Archimedean
Faces	4 triangles 4 hexagons
Edges	18
Vertices	12
Vertex configuration	3,6,6
Symmetry group	tetrahedral (Td)
Dual polyhedron	triakis tetrahedron
Properties	convex, semi-regular (vertex-uniform)

The truncated tetrahedron is an Archimedean solid. Canonical coordinates for the vertices of a truncated tetrahedron centered at the origin are (±3, ±1, ±1), (±1, ±3, ±1), (±1, ±1, ±3), where the ± has the same parity for each coordinate, that is, all coordinates have an even number of minuses (or all have an odd number).

Truncated_tetrahedron_flat.png
image:truncated tetrahedron flat.png

It has 4 regular hexagonal faces, 4 regular triangular faces, 12 vertices and 18 edges.

A famous depiction of an irregular truncated tetrahedron is in Albrecht Dürer's engraving, "Melencolia I". See illustration at entry Melancholy.

See also

• octahedron
• tetrahedron

External links

• The Uniform Polyhedra (http://www.mathconsult.ch/showroom/unipoly/)
• Virtual Reality Polyhedra (http://www.georgehart.com/virtual-polyhedra/vp.html) The Encyclopedia of Polyhedra