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50th Johnson solid From Wikipedia, the free encyclopedia
In geometry, the biaugmented triangular prism is a polyhedron constructed from a triangular prism by attaching two equilateral square pyramids onto two of its square faces. It is an example of Johnson solid. It can be found in stereochemistry in bicapped trigonal prismatic molecular geometry.
The biaugmented triangular prism can be constructed from a triangular prism by attaching two equilateral square pyramids onto its two square faces, a process known as augmentation.[1] These pyramids covers the square face of the prism, so the resulting polyhedron has 10 equilateral triangles and 1 square as its faces.[2] A convex polyhedron in which all faces are regular polygons is Johnson solid. The biaugmented triangular prism is among them, enumerated as 50th Johnson solid .[3]
A biaugmented triangular prism with edge length has a surface area, calculated by adding ten equilateral triangles and one square's area:[2] Its volume can be obtained by slicing it into a regular triangular prism and two equilateral square pyramids, and adding their volumes subsequently:[2]
It has three-dimensional symmetry group of the cyclic group of order 4. Its dihedral angle can be calculated by adding the angle of an equilateral square pyramid and a regular triangular prism in the following:[4]
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. An example of such structure is plutonium(III) bromide PuBr3 adopted by bromides and iodides of the lanthanides and actinides.[5]
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