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The cube can be dissected into six 3-orthoschemes, three left-handed and three right-handed (one of each at each cube face), and cubes can fill space, so the characteristic 3-orthoscheme of the cube is a space-filling tetrahedron in this sense.
A trirectangular tetrahedron with its base shown in green and its apex as a solid black disk. It can be constructed by a coordinate octant and a plane crossing all 3 axes away from the origin (x>0; y>0; z>0) and x/a+y/b+z/c<1. In geometry, a trirectangular tetrahedron is a tetrahedron where all three face angles at one vertex are right angles.
Regular polyhedron. Platonic solid: . Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot ...
Tetrahedron {3,3} (3.3.3) arccos ( 1 / 3 ) 70.529° Hexahedron or Cube {4,3} (4.4.4) arccos (0) = π / 2 90° Octahedron {3,4} (3.3.3.3) arccos (- 1 / 3 ) 109.471° Dodecahedron {5,3} (5.5.5) arccos (- √ 5 / 5 ) 116.565° Icosahedron {3,5} (3.3.3.3.3) arccos (- √ 5 / 3 ) 138.190° Kepler–Poinsot solids ...
In geometry, the Möbius configuration or Möbius tetrads is a certain configuration in Euclidean space or projective space, consisting of two tetrahedra that are mutually inscribed: each vertex of one tetrahedron lies on a face plane of the other tetrahedron and vice versa. Thus, for the resulting system of eight points and eight planes, each ...
The triakis tetrahedron can be seen as a tetrahedron with a triangular pyramid added to each face; that is, it is the Kleetope of the tetrahedron. It is very similar to the net for the 5-cell, as the net for a tetrahedron is a triangle with other triangles added to each edge, the net for the 5-cell a tetrahedron with pyramids attached to each ...
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.
T h, 3*2, [4,3 +] or m 3, of order 24 – pyritohedral symmetry. [1] This group has the same rotation axes as T, with mirror planes through two of the orthogonal directions. The 3-fold axes are now S 6 ( 3 ) axes, and there is a central inversion symmetry.