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The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid , which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point.
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices.
Three dimensional Three-dimensional space. Regular. Regular polyhedron ... Hexagonal prism, Truncated tetrahedron, Tetragonal trapezohedron; Enneahedron.
Tetrahedron {3, 3} Cube {4, 3} Octahedron {3, 4} ... polyhedra were firmly understood as three-dimensional examples of more general polytopes in any number of dimensions.
The three-dimensional analog of a plane angle is a solid angle. ... these coincide with the tetrahedron as {3,3}, the cube as {4,3}, and the octahedron as {3,4}. See also
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. The 4 solid angles - associated to each point of the tetrahedron.
The basic 3-dimensional element are the tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron. They all have triangular and quadrilateral faces. Extruded 2-dimensional models may be represented entirely by the prisms and hexahedra as extruded triangles and quadrilaterals. In general, quadrilateral faces in 3-dimensions may not be ...
They can be seen inside as points on and within a cube, {4,3}. In geometry, a Goursat tetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane on 3-dimensional surfaces: the 3-sphere, Euclidean 3-space, and hyperbolic 3-space.