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Disphenocingulum
In geometry, the disphenocingulum or pentakis elongated gyrobifastigium is one of the Johnson solids (). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. Cartesian coordinates Let ''a'' ≈ 0.76713 be the second smallest positive root of the polynomial : \begin &256x^ - 512x^ - 1664x^ + 3712x^9 + 1552x^8 - 6592x^7 \\ &\quad + 1248x^6 + 4352x^5 - 2024x^4 - 944x^3 + 672x^2 - 24x - 23 \end and h = \sqrt and c = \sqrt. Then, Cartesian coordinates of a disphenocingulum with edge length 2 are given by the union of the orbits of the points :\left(1,2a,\frac\right),\ \left(1,0,2c+\frac\right),\ \left(1+\frac,0,2c-\frac+\frac\right) under the action of the group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the sa ... [...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] |
