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The 6 edge lengths - associated to the six edges of the tetrahedron. The 12 face angles - there are three of them for each of the four faces of the tetrahedron. The 6 dihedral angles - associated to the six edges of the tetrahedron, since any two faces of the tetrahedron are connected by an edge.
Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. ... Clearly the sum of the angles of any side of the tetrahedron must be 180°.
It is also the symmetry of a pyritohedron, which is extremely similar to the cube described, with each rectangle replaced by a pentagon with one symmetry axis and 4 equal sides and 1 different side (the one corresponding to the line segment dividing the cube's face); i.e., the cube's faces bulge out at the dividing line and become narrower there.
The tetrahedron is self-dual, i.e. it pairs with itself. The cube and octahedron are dual to each other. The icosahedron and dodecahedron are dual to each other. The small stellated dodecahedron and great dodecahedron are dual to each other. The great stellated dodecahedron and great icosahedron are dual to each other.
A pyramid with side length 5 contains 35 spheres. Each layer represents one of the first five triangular numbers. A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.
Tetrahedron; Cube; Octahedron; Dodecahedron; Icosahedron; Kepler–Poinsot polyhedron (regular star polyhedra) Great icosahedron; Small stellated dodecahedron; Great dodecahedron; Great stellated dodecahedron; Abstract regular polyhedra (Projective polyhedron) Hemicube; Hemi-octahedron; Hemi-dodecahedron; Hemi-icosahedron; Archimedean solid ...
The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids , Archimedean solids , Catalan solids , and Johnson solids , as well as dihedral symmetry families including the pyramids , bipyramids , prisms , antiprisms , and trapezohedrons .
In geometry, an orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular. It is also known as an orthogonal tetrahedron since orthogonal means perpendicular. It was first studied by Simon Lhuilier in 1782, and got the name orthocentric tetrahedron by G. de Longchamps in 1890. [1]