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Gyroelongated Square Cupola
In geometry, the gyroelongated square cupola is one of the Johnson solids (''J''23). As the name suggests, it can be constructed by gyroelongation, gyroelongating a square cupola (''J''4) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (''J''45) with one square bicupola removed. Area and Volume The surface area is, :A=\left(7+2\sqrt+5\sqrt\right)a^2\approx 18.4886811...a^2. The volume is the sum of the volume of a square cupola and the volume of an octagonal prism, :V=\left(1+\frac\sqrt + \frac\sqrt\right)a^3\approx6.2107658...a^3. Dual polyhedron The dual of the gyroelongated square cupola has 20 faces: 8 kites, 4 rhombi, and 8 pentagons. External links * {{Johnson solids navigator Johnson solids ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), vertex. An example of a Johnson solid is the square-based Pyramid (geometry), pyramid with equilateral sides (square pyramid, ); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform polyhedron, uniform (i.e., not Platonic solid, Archimedean solid, prism (geometry), uniform prism, or uniform antiprism) before they refer to it as a “Johnson solid”. As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex. The pentagonal pyramid () is an example that has a degree-5 vertex. Although there is no obvious restriction tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
