Augmented truncated tetrahedron
| Augmented truncated tetrahedron | |
|---|---|
 | |
| Type | Johnson J64 – J65 – J66 |
| Faces | 2+2x3 triangles 3 squares 3 hexagons |
| Edges | 27 |
| Vertices | 15 |
| Vertex configuration | 2x3(3.62) 3(3.4.3.4) 6(3.4.3.6) |
| Symmetry group | C3v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the augmented truncated tetrahedron is a polyhedron constructed by attaching a triangular cupola onto an truncated tetrahedron. It is an example of a Johnson solid.
Construction
The augmented truncated tetrahedron is constructed from a truncated tetrahedron by attaching a triangular cupola.[1] This cupola covers the hexagonal face so that the resulting polyhedron has the face of twelve equilateral triangles, three squares, and 3 regular hexagons.[2] Since it has the property of convexity and has regular polygonal faces, the augmented truncated tetrahedron is a Johnson solid, denoted as the sixty-fifth Johnson solid .[3]
References
- ^ Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. p. 84–89. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.
- ^ Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
- ^ Francis, Darryl (August 2013). "Johnson solids & their acronyms". Word Ways. 46 (3): 177.
External links
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