Laplace–Runge–Lenz vector
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In geometry, a triakis tetrahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated tetrahedron.
It can be seen as a tetrahedron with triangular pyramids added to each face; that is, it is the Kleetope of the tetrahedron. This interpretation is expressed in the name.
If the triakis tetrahedron has shorter edge lengths 1, it has area and volume .
Orthogonal projections
| Centered by | Edge normal | Face normal | Edge | Face/vertex |
|---|---|---|---|---|
| Truncated tetrahedron |
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| Triakis tetrahedron |
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| Projective symmetry |
[1] | [1] | [3] | [4] |
Variations
A triakis tetrahedron with equilateral triangle faces represents a net of the four-dimensional regular polytope known as the 5-cell.
Stellations
This chiral figure is one of thirteen stellations allowed by Miller's rules.
Related polyhedra
The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These face-transitive figures have (*n32) reflectional symmetry.
Template:Truncated figure1 table
See also
References
- Template:The Geometrical Foundation of Natural Structure (book) (Section 3-9)
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