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  2. Heptagon - Wikipedia

    en.wikipedia.org/wiki/Heptagon

    In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.

  3. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. ... 7: 5{4} +2{5} Hexagonal prism: 4.4.6:

  4. Heptahedron - Wikipedia

    en.wikipedia.org/wiki/Heptahedron

    There are 34 topologically distinct convex heptahedra, excluding mirror images. [2] ( 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 lengths of edges or the angles between edges or faces.)

  5. Rhombicosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicosidodecahedron

    Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √ φ 6 +2 = √ 8φ+7 for edge length 2. For unit edge length, R must be halved, giving R = ⁠ √ 8φ+7 / 2 ⁠ = ⁠ √ 11+4 √ 5 / 2 ⁠ ≈ 2.233.

  6. Platonic solid - Wikipedia

    en.wikipedia.org/wiki/Platonic_solid

    By a theorem of Descartes, this is equal to 4 π divided by the number of vertices (i.e. the total defect at all vertices is 4 π). The three-dimensional analog of a plane angle is a solid angle. The solid angle, Ω, at the vertex of a Platonic solid is given in terms of the dihedral angle by

  7. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    The elements of the set correspond to the vertices, edges, faces and so on of the polytope: vertices have rank 0, edges rank 1, etc. with the partially ordered ranking corresponding to the dimensionality of the geometric elements. The empty set, required by set theory, has a rank of −1 and is sometimes said to correspond to the null polytope.

  8. Star polygon - Wikipedia

    en.wikipedia.org/wiki/Star_polygon

    The density of a polygon can also be called its turning number: the sum of the turn angles of all the vertices, divided by 360°. The symmetry group of {p/q} is the dihedral group D p, of order 2p, independent of q. Regular star polygons were first studied systematically by Thomas Bradwardine, and later Johannes Kepler. [4]

  9. Vertex (geometry) - Wikipedia

    en.wikipedia.org/wiki/Vertex_(geometry)

    A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]