Английская Википедия:Elongated triangular pyramid
Шаблон:Short description Шаблон:Infobox polyhedron
In geometry, the elongated triangular pyramid is one of the Johnson solids (Шаблон:Math). As the name suggests, it can be constructed by elongating a tetrahedron by attaching a triangular prism to its base. Like any elongated pyramid, the resulting solid is topologically (but not geometrically) self-dual.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]
- <math>V=\left(\frac{1}{12}\left(\sqrt{2}+3\sqrt{3}\right)\right)a^3\approx0.550864...a^3</math>
- <math>A=\left(3+\sqrt{3}\right)a^2\approx4.73205...a^2</math>
- <math>H = a\cdot \left( 1 + \frac{\sqrt{6}}{3}\right) \approx a\cdot 1.816496581</math>
If the edges are not the same length, use the individual formulae for the tetrahedron and triangular prism separately, and add the results together.
Dual polyhedron
Topologically, the elongated triangular pyramid is its own dual. Geometrically, the dual has seven irregular faces: one equilateral triangle, three isosceles triangles and three isosceles trapezoids.
| Dual elongated triangular pyramid | Net of dual |
|---|---|
| Файл:Dual elongated triangular pyramid.png | Файл:Dual elongated triangular pyramid net.png |
Related polyhedra and honeycombs
The elongated triangular pyramid can form a tessellation of space with square pyramids and/or octahedra.[3]
References
External links
Шаблон:Johnson solids navigator
- ↑ Stephen Wolfram, "Elongated triangular pyramid" from Wolfram Alpha. Retrieved July 21, 2010.
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite web
