Biaugmented pentagonal prism | |
---|---|
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Type |
Johnson J52 – J53 – J54 |
Faces | 8
equilateral triangles 3 squares 2 pentagons |
Edges | 23 |
Vertices | 12 |
Vertex configuration | 2(42.5) 2(34) 2x4(32.4.5) |
Symmetry group | C2v |
Properties | convex |
Net | |
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In geometry, the biaugmented pentagonal prism is a polyhedron constructed from a pentagonal prism by attaching two equilateral square pyramids onto each of its square faces. It is an example of Johnson solid.
The biaugmented pentagonal prism can be constructed from a pentagonal prism by attaching two equilateral square pyramids to each of its square faces, a process known as augmentation. [1] These square pyramids cover the square face of the prism, so the resulting polyhedron has eight equilateral triangles, three squares, and two regular pentagons as its faces. [2] A convex polyhedron in which all faces are regular is Johnson solid, and the augmented pentagonal prism is among them, enumerated as 53rd Johnson solid . [3]
An biaugmented pentagonal prism with edge length has a surface area, calculated by adding the area of four equilateral triangles, four squares, and two regular pentagons: [2] Its volume can be obtained by slicing it into a regular pentagonal prism and an equilateral square pyramid, and adding their volume subsequently: [2]
The dihedral angle of an augmented pentagonal prism can be calculated by adding the dihedral angle of an equilateral square pyramid and the regular pentagonal prism: [4]
Biaugmented pentagonal prism | |
---|---|
![]() | |
Type |
Johnson J52 – J53 – J54 |
Faces | 8
equilateral triangles 3 squares 2 pentagons |
Edges | 23 |
Vertices | 12 |
Vertex configuration | 2(42.5) 2(34) 2x4(32.4.5) |
Symmetry group | C2v |
Properties | convex |
Net | |
![]() |
In geometry, the biaugmented pentagonal prism is a polyhedron constructed from a pentagonal prism by attaching two equilateral square pyramids onto each of its square faces. It is an example of Johnson solid.
The biaugmented pentagonal prism can be constructed from a pentagonal prism by attaching two equilateral square pyramids to each of its square faces, a process known as augmentation. [1] These square pyramids cover the square face of the prism, so the resulting polyhedron has eight equilateral triangles, three squares, and two regular pentagons as its faces. [2] A convex polyhedron in which all faces are regular is Johnson solid, and the augmented pentagonal prism is among them, enumerated as 53rd Johnson solid . [3]
An biaugmented pentagonal prism with edge length has a surface area, calculated by adding the area of four equilateral triangles, four squares, and two regular pentagons: [2] Its volume can be obtained by slicing it into a regular pentagonal prism and an equilateral square pyramid, and adding their volume subsequently: [2]
The dihedral angle of an augmented pentagonal prism can be calculated by adding the dihedral angle of an equilateral square pyramid and the regular pentagonal prism: [4]