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It can be seen as a truncated hexagonal hosohedron, represented by Schläfli symbol t{2,6}. Alternately it can be seen as the Cartesian product of a regular hexagon and a line segment, and represented by the product {6}×{}. The dual of a hexagonal prism is a hexagonal bipyramid. The symmetry group of a right hexagonal prism is D 6h of order 24.
The edge-first parallel projection of the tesseract into three-dimensional space has an envelope in the shape of a hexagonal prism. Six cells project onto rhombic prisms, which are laid out in the hexagonal prism in a way analogous to how the faces of the 3D cube project onto six rhombs in a hexagonal envelope under vertex-first projection.
The remaining hexagonal prisms are projected to 12 non-regular hexagonal prism images, lying where a cube's edges would be. Each image corresponds to two cells. Finally, the 8 volumes between the hexagonal faces of the projection envelope and the hexagonal faces of the central truncated cuboctahedron are the images of the 16 truncated octahedra ...
Related square and triangular prism structures in three and four directions, are named by Conway as tetrastix and "tristix". If the ends of the prisms in a hexastix arrangement are pointed, the directionality modifies the symmetry and the related structure is known as hexastakes [ 1 ] .
The rectified hexagonal tiling honeycomb, t 1 {6,3,3}, has tetrahedral and trihexagonal tiling facets, with a triangular prism vertex figure. The half-symmetry construction alternates two types of tetrahedra.
The elongated triangular cupola is constructed from a hexagonal prism by attaching a triangular cupola onto one of its bases, a process known as the elongation. [1] This cupola covers the hexagonal face so that the resulting polyhedron has four equilateral triangles, nine squares, and one regular hexagon. [2]
Plane "hexagonal cupolae" in the rhombitrihexagonal tilingThe triangular, square, and pentagonal cupolae are the only non-trivial convex cupolae with regular faces: The "hexagonal cupola" is a plane figure, and the triangular prism might be considered a "cupola" of degree 2 (the cupola of a line segment and a square).
A quartz crystal is an example of an elongated hexagonal bipyramid. Because it has 18 faces, it can be called an octadecahedron. Other chemicals also have this shape. [1] The edge-first orthogonal projection of a 24-cell is an elongated hexagonal bipyramid. Used as the shape of Fruit Gushers candy.