Triangular prism

Apr 23, 2026 - 09:37
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Triangular prism

As a uniform prism: Whoops, forgot another 1/2.

← Previous revision Revision as of 04:05, 23 April 2026
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{{harvp|Haul|1893|p=[https://archive.org/details/mensuration00hallgoog/page/n57 45]}}
{{harvp|Haul|1893|p=[https://archive.org/details/mensuration00hallgoog/page/n57 45]}}
}}
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V = \frac{1}{2}bh \cdot l = \frac{bhl}{2},
V = \frac{1}{2}bh \cdot l.
In the case of a right triangular prism, where all its edges are equal in length {{math|1=''l''}}, its volume can be calculated as the product of the equilateral triangle's area and the distance between bases:{{sfnp|Berman|1971}}
In the case of a right triangular prism, where all its edges are equal in length {{math|1=''l''}}, its volume can be calculated as the product of the equilateral triangle's area and the distance between bases:{{sfnp|Berman|1971}}
V_\text{uniform} = \frac{\sqrt{3}}{2}l^2 \cdot l \approx 0.433l^3
V_\text{uniform} = \frac{1}{2} \cdot \frac{\sqrt{3}}{2}l^2 \cdot l \approx 0.433l^3


The [[Point groups in three dimensions|three-dimensional symmetry group]] of a triangular prism is [[dihedral group]] {{math|1=''D''3''h''}} of order 12: the appearance is unchanged if the triangular prism is rotated one- and two- thirds of a full angle around its [[axis of symmetry]] passing through the center's base, and reflecting across a horizontal plane.{{sfnp|Johnson|1966}} The [[dual polyhedron]] of any prism is a [[Bipyramid|bipyramid]], a polyhedron formed by fusing two pyramids base-to-base. In the case of a triangular prism, its dual is a [[triangular bipyramid]], both of which have a common three-dimensional symmetry group.{{sfnp|King|1994|p=[https://books.google.com/books?id=c3fsCAAAQBAJ&pg=PA113 113]}}
The [[Point groups in three dimensions|three-dimensional symmetry group]] of a triangular prism is [[dihedral group]] {{math|1=''D''3''h''}} of order 12: the appearance is unchanged if the triangular prism is rotated one- and two- thirds of a full angle around its [[axis of symmetry]] passing through the center's base, and reflecting across a horizontal plane.{{sfnp|Johnson|1966}} The [[dual polyhedron]] of any prism is a [[Bipyramid|bipyramid]], a polyhedron formed by fusing two pyramids base-to-base. In the case of a triangular prism, its dual is a [[triangular bipyramid]], both of which have a common three-dimensional symmetry group.{{sfnp|King|1994|p=[https://books.google.com/books?id=c3fsCAAAQBAJ&pg=PA113 113]}}
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