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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 .
[21] The simplest polygon which can exist as a regular star. A star pentagon is known as a pentagram or pentacle. hexagon: 6 [21] Can tile the plane. heptagon (or septagon) 7 [21] The simplest polygon such that the regular form is not constructible with compass and straightedge. However, it can be constructed using a neusis construction ...
A non-convex regular polygon is a regular star polygon. The most common example is the pentagram , which has the same vertices as a pentagon , but connects alternating vertices. For an n -sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as { n / m }.
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra:
A regular dihedron, {n, 2} [13] (2-hedron) in three-dimensional Euclidean space can be considered a degenerate prism consisting of two (planar) n-sided polygons connected "back-to-back", so that the resulting object has no depth, analogously to how a digon can be constructed with two line segments.
Three mutually perpendicular golden ratio rectangles, with edges connecting their corners, form a regular icosahedron. Another way to construct it is by putting two points on each surface of a cube. In each face, draw a segment line between the midpoints of two opposite edges and locate two points with the golden ratio distance from each midpoint.
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A regular n-gon has a solid construction if and only if n=2 a 3 b m where a and b are some non-negative integers and m is a product of zero or more distinct Pierpont primes (primes of the form 2 r 3 s +1). Therefore, regular n-gon admits a solid, but not planar, construction if and only if n is in the sequence