User:Dedhert.Jr/sandbox/2

Types of tetrahedra

A tetrahedron is a three-dimensional object with four faces, six edges, and four vertices. It can be considered as pyramid whenever one of its faces can be considered as the base. There are many types of tetrahedra. A trirectangular tetrahedron is a tetrahedron whose three face angles at one vertex are right angles, as at the corner of a cube. A disphenoid is a tetrahedron whose four faces are congruent acute-angled triangles, a special case of a regular tetrahedron.

Generally, the tetrahedron can be seen as a wheel graph, meaning it is a triangle in which three vertices connect its center known as the universal vertex in a plane. Unlike other pyramids and other polyhedrons, the tetrahedron is one of the polyhedrons that does not have space diagonal; the other polyhedrons with such property are Császár polyhedron and Schonhardt polyhedron. It is also known as 3-simplex, the generalization of a triangle in multi-dimension. It is self-dual, meaning its dual polyhedron is tetrahedron itself. Many other properties of tetrahedra are explicitly described in the following sections.

Bibliography

• Alsina, C.; Nelsen, R. B. (2015). A Mathematical Space Odyssey: Solid Geometry in the 21st Century. Mathematical Association of America. ISBN 978-1-61444-216-5.
• Bottema, O. (1969). "A Theorem of Bobillier on the Tetrahedron". Elemente der Mathematik. 24: 6–10.
• Coxeter, H. S. M. (1948). Regular Polytopes. Methuen and Co.
• Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York: Dover Publications.
• Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. ISBN 978-0-521-55432-9.
• Cundy, H. Martyn (1952). "Deltahedra". The Mathematical Gazette. 36 (318): 263–266. doi:10.2307/3608204. JSTOR 3608204. S2CID 250435684.
• Fekete, A. E. (1985). Real Linear Algebra. Marcel Dekker Inc. ISBN 978-0-8247-7238-3.
• Kahan, W. M. (2012). What has the Volume of a Tetrahedron to do with Computer Programming Languages? (PDF) (Thesis). pp. 16–17.
• Kepler, Johannes (1619). Harmonices Mundi (The Harmony of the World). Johann Planck.
• Lee, Jung Rye (1997). "The Law of Cosines in a Tetrahedron". J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 4 (1): 1–6.
• Murakami, Jun; Yano, Masakazu (2005). "On the volume of a hyperbolic and spherical tetrahedron". Communications in Analysis and Geometry. 13 (2): 379–400. doi:10.4310/cag.2005.v13.n2.a5. ISSN 1019-8385. MR 2154824.
• Park, Poo-Sung (2016). "Regular polytope distances" (PDF). Forum Geometricorum. 16: 227–232.
• Shavinina, Larisa V. (2013). The Routledge International Handbook of Innovation Education. Routledge. ISBN 978-0-203-38714-6.