|
Tetrakaidecahedron
240px, A tetradecahedron with D2d-symmetry, existing in the Weaire–Phelan structure A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces. A tetradecahedron is sometimes called a tetrakaidecahedron. No difference in meaning is ascribed. The Greek word '' kai'' means 'and'. There is evidence that mammalian epidermal cells are shaped like flattened tetrakaidecahedra, an idea first suggested by Lord Kelvin. The polyhedron can also be found in soap bubbles and in sintered ceramics, due to its ability to tesselate in 3D space. Convex There are 1,496,225,352 topologically distinct ''convex'' tetradecahedra, excluding mirror images, having at least 9 vertices. (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Tetrakaidecahedron
{{disambiguation ...
Space filling or spacefilling may refer to: *Space-filling curve *Space-filling model, in chemistry *Space-filling polyhedron *Space-filling tree *Space-filling bubble in a foam Foams are two-phase materials science, material systems where a gas is dispersed in a second, non-gaseous material, specifically, in which gas cells are enclosed by a distinct liquid or solid material. Note, this source focuses only on liquid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prism (geometry)
In geometry, a prism is a polyhedron comprising an polygon Base (geometry), base, a second base which is a Translation (geometry), translated copy (rigidly moved without rotation) of the first, and other Face (geometry), faces, necessarily all parallelograms, joining corresponding sides of the two bases. All Cross section (geometry), cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. Like many basic geometric terms, the word ''prism'' () was first used in Euclid's Elements, Euclid's ''Elements''. Euclid defined the term in Book XI as "a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms". However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilunabirotunda
In geometry, the bilunabirotunda is a Johnson solid with faces of 8 equilateral triangles, 2 squares, and 4 regular pentagons. Properties The bilunabirotunda is named from the prefix ''lune'', meaning a figure featuring two triangles adjacent to opposite sides of a square. Therefore, the faces of a bilunabirotunda possess 8 equilateral triangles, 2 squares, and 4 regular pentagons as it faces. It is one of the Johnson solids—a convex polyhedron in which all of the faces are regular polygon—enumerated as 91st Johnson solid J_ . The surface area of a bilunabirotunda with edge length a is: \left(2 + 2\sqrt + \sqrt\right)a^2 \approx 12.346a^2, and the volume of a bilunabirotunda is: \fraca^3 \approx 3.0937a^3. Construction The bilunabirotunda is an elementary polyhedron: it cannot be separated by a plane into two small regular-faced polyhedra. One way to construct a bilunabirotunda is by attaching two wedges and two tridiminished icosahedrons. For edge lengt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphenocorona
In geometry, the sphenocorona is a Johnson solid with 12 equilateral triangles and 2 squares as its faces. Properties The sphenocorona was named by in which he used the prefix ''spheno-'' referring to a wedge-like complex formed by two adjacent '' lunes''—a square with equilateral triangles attached on its opposite sides. The suffix ''-corona'' refers to a crownlike complex of 8 equilateral triangles. By joining both complexes together, the resulting polyhedron has 12 equilateral triangles and 2 squares, making 14 faces. A convex polyhedron in which all faces are regular polygons is called a Johnson solid. The sphenocorona is among them, enumerated as the 86th Johnson solid J_ . It is an elementary polyhedron, meaning it cannot be separated by a plane into two small regular-faced polyhedra. The surface area of a sphenocorona with edge length a can be calculated as: A=\left(2+3\sqrt\right)a^2\approx7.19615a^2, and its volume as: \left(\frac\sqrt\right)a^3\approx1.51 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augmented Truncated Tetrahedron
In geometry, the augmented truncated tetrahedron is a polyhedron constructed by attaching a triangular cupola onto a truncated tetrahedron. It is an example of a Johnson solid. Construction The augmented truncated tetrahedron is constructed from a truncated tetrahedron by attaching a triangular cupola In geometry, the triangular cupola is the cupola with hexagon as its base and triangle as its top. If the edges are equal in length, the triangular cupola is the Johnson solid. It can be seen as half a cuboctahedron. The triangular cupola can b .... This cupola covers one of the truncated tetrahedron's four hexagonal faces, so that the resulting polyhedron's faces are eight equilateral triangles, three squares, and three regular hexagons. Since it has the property of Convex set, convexity and has regular polygonal faces, the augmented truncated tetrahedron is a Johnson solid, denoted as the sixty-fifth Johnson solid J_ . Properties The surface area of an augmented truncat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
