Triaugmented triangular prism: Difference between revisions

Revision as of 00:26, 26 November 2022

Revision as of 01:31, 26 November 2022

Line 40:

can be derived by slicing it into a central prism and three square pyramids, and adding their volumes.

It has the same [[Point groups in three dimensions|three-dimensional symmetry group]] as the triangular prism, the [[dihedral group]] <math>D_{3\mathrm{h}}</math> of order twelve. Its [[dihedral angle]]s can be calculated by adding the angles of the component pyramids and prism:. The prism itself has square-triangle dihedral angles <math>\pi/2</math> and square-square angles <math>\pi/3</math>,. andThe thetriangle-triangle pyramidangles hason dihedralthe anglespyramid ofare halfthe thatsame as ofin the [[regular octahedron]], and the square-triangle angles are half that. Therefore, for the triaugmented triangular prism, the dihedral angles incident to the degree-four vertices, on the edges of the prism triangles, and on the square-to-square prism edges are, respectively,{{r|johnson}}

<math display=block>

\begin{align}