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The augmented hexagonal prism is constructed by attaching one equilateral square pyramid onto the square face of a hexagonal prism, a process known as augmentation. [1] This construction involves the removal of the prism square face and replacing it with the square pyramid, so that there are eleven faces: four equilateral triangles, five squares, and two regular hexagons. [2]
In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids (J 55). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids ( J 1 ) to two of its nonadjacent, parallel (opposite) equatorial faces.
In geometry, the triaugmented hexagonal prism is one of the Johnson solids (J 57). As the name suggests, it can be constructed by triply augmenting a hexagonal prism by attaching square pyramids ( J 1 ) to three of its nonadjacent equatorial faces.
A triaugmented triangular prism with edge length has surface area [10], the area of 14 equilateral triangles. Its volume, [ 10 ] 2 2 + 3 4 a 3 ≈ 1.140 a 3 , {\displaystyle {\frac {2{\sqrt {2}}+{\sqrt {3}}}{4}}a^{3}\approx 1.140a^{3},} can be derived by slicing it into a central prism and three square pyramids, and adding their volumes.
the dihedral angle of an elongated triangular cupola between two adjacent squares is that of a hexagonal prism, the internal angle of its base 120°; the dihedral angle of a hexagonal prism between square-to-hexagon is 90°, that of a triangular cupola between square-to-hexagon is 54.7°, and that of a triangular cupola between triangle-to ...
As the name suggests, it can be constructed by elongating a pentagonal pyramid (J 2) by attaching a pentagonal prism to its base. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids , Archimedean solids , prisms , or antiprisms ).
An augmented triangular prism with edge length has a surface area, calculated by adding six equilateral triangles and two squares' area: [2] +. Its volume can be obtained by slicing it into a regular triangular prism and an equilateral square pyramid, and adding their volume subsequently: [ 2 ] 2 2 + 3 3 12 a 3 ≈ 0.669 a 3 . {\displaystyle ...
A diminished cube, realized with 4 equilateral-triangle and 3 kite faces, all having the same area, [1] A heptahedron (pl.: heptahedra) is a polyhedron having seven sides, or faces. A heptahedron can take a large number of different basic forms, or topologies. The most familiar are the hexagonal pyramid and the pentagonal prism.