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Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and ...
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices , and 120 edges .
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding ...
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
Given a unit sphere, a "spherical triangle" on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere (shown at right). If the lengths of these three sides are a (from u to v ), b (from u to w ), and c (from v to w ), and the angle of the corner opposite c is C , then the (first) spherical ...
In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides and two vertices.Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space.
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere [a] or the n-dimensional surface of higher dimensional spheres.
In Magnus Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+} b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, and q-valence vertices. The + symbol indicates the valence of the vertices being increased.