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In geometry, a triangular prism or trigonal prism [1] is a prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a right triangular prism. A right triangular prism may be both semiregular and uniform. The triangular prism can be used in constructing another polyhedron.
The dual polyhedron of the triaugmented triangular prism has a face for each vertex of the triaugmented triangular prism, and a vertex for each face. It is an enneahedron (that is, a nine-sided polyhedron) [ 16 ] that can be realized with three non-adjacent square faces, and six more faces that are congruent irregular pentagons . [ 17 ]
An oblique prism is a prism in which the joining edges and faces are not perpendicular to the base faces. Example: a parallelepiped is an oblique prism whose base is a parallelogram, or equivalently a polyhedron with six parallelogram faces. Right Prism. A right prism is a prism in which the joining edges and faces are perpendicular to the base ...
A triangular bipyramid is the dual polyhedron of a triangular prism, and vice versa. [17] [3] A triangular prism has five faces, nine edges, and six vertices, with the same symmetry as a triangular bipyramid. [3]
The biaugmented triangular prism can be found in stereochemistry, as a structural shape of a chemical compound known as bicapped trigonal prismatic molecular geometry.It is one of the three common shapes for transition metal complexes with eight vertices other than the chemical structure other than square antiprism and the snub disphenoid.
b = the base side of the prism's triangular base, h = the height of the prism's triangular base L = the length of the prism see above for general triangular base Isosceles triangular prism: b = the base side of the prism's triangular base, h = the height of the prism's triangular base
The dihedral angle of an augmented triangular prism between square and triangle is the dihedral angle of a triangular prism between the base and its lateral face, / = The dihedral angle of an equilateral square pyramid between a triangular face and its base is arctan ( 2 ) ≈ 54.7 ∘ {\textstyle \arctan \left({\sqrt {2}}\right)\approx 54. ...
In the case of 3-3 duoprism is the simplest among them, and it can be constructed using Cartesian product of two triangles. The resulting duoprism has 9 vertices, 18 edges, [2] and 15 faces—which include 9 squares and 6 triangles. Its cell has 6 triangular prism. It has Coxeter diagram, and symmetry [[3,2,3]], order 72.