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In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape is also called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron.
It can be seen as a dodecahedron with three pentagonal pyramids (J 2) attached to nonadjacent faces. When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron ( J 58 ), a parabiaugmented dodecahedron ( J 59 ), a metabiaugmented dodecahedron ( J 60 ), or even a pentakis dodecahedron if the faces are ...
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
In geometry, a dodecahedral prism is a convex uniform 4-polytope. This 4-polytope has 14 polyhedral cells: 2 dodecahedra connected by 12 pentagonal prisms. It has 54 faces: 30 squares and 24 pentagons. It has 80 edges and 40 vertices.
As its name suggests, it is created by attaching three pentagonal cupolas (J 5) onto three nonadjacent decagonal faces of a truncated dodecahedron. 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 ...
The rhombic dodecahedron is a Voronoi cell of the other optimal way to stack spheres. The two shapes differ in their combinatorial structure as well as in their geometry: in the rhombic dodecahedron, every edge connects a degree-three vertex to a degree-four vertex, whereas the trapezo-rhombic dodecahedron has six edges that connect vertices of ...
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.
In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (J 83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed. 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 ...