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Packing circles in an isosceles right triangle - good estimates are known for n < 300. Packing circles in an equilateral triangle - Optimal solutions are known for n < 13 , and conjectures are available for n < 28 .
Each triangle can be mapped to another triangle of the same color by means of a 3D rotation alone. Triangles of different colors can be mapped to each other with a reflection or inversion in addition to rotations. Disdyakis triacontahedron hulls. The 62 vertices of a disdyakis triacontahedron are given by: [2]
In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edge s and face s that defines the shape of a polyhedral object's surface. It simplifies rendering, as in a wire-frame model. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons .
The Kepler triangle is a right triangle whose sides are in geometric progression. If the sides are formed from the geometric progression a, ar, ar 2 then its common ratio r is given by r = √ φ where φ is the golden ratio. Its sides are therefore in the ratio 1 : √ φ : φ. Thus, the shape of the Kepler triangle is uniquely determined (up ...
STL is a file format native to the stereolithography CAD software created by 3D Systems. [3] [4] [5] Chuck Hull, the inventor of stereolithography and 3D Systems’ founder, reports that the file extension is an abbreviation for stereolithography, [6] although it is also referred to as standard triangle language or standard tessellation language.
The concept of a triangulation may also be generalized somewhat to subdivisions into shapes related to triangles. In particular, a pseudotriangulation of a point set is a partition of the convex hull of the points into pseudotriangles—polygons that, like triangles, have exactly three convex vertices. As in point set triangulations ...
3D model of regular octahedron. ... , a right triangle with edges , , , and a right triangle with edges ... This group's subgroups include D 3d ...
A 3-orthoscheme is a tetrahedron where all four faces are right triangles. A 3-orthoscheme is not a disphenoid, because its opposite edges are not of equal length. It is not possible to construct a disphenoid with right triangle or obtuse triangle faces.
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