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A Froebel star. The three-dimensional Froebel star is assembled from four identical paper strips with a width-to-length proportion of between 1:25 and 1:30. [2] The weaving and folding procedure can be accomplished in about forty steps. The product is a paper star with eight flat prongs and eight cone-shaped tips.
Star polygon, a star drawn with a number of lines equal to the number of points Pentagram, a five-pointed star polygon Five-pointed star, a pentagram with internal line segments removed; Lute of Pythagoras, a pentagram-based fractal pattern; Hexagram, a six-pointed star polygon; Heptagram, a seven-pointed star polygon
A truncated square is an octagon, t{4}={8}. A quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}. [2] The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces constructed from the cube in this way. It may be considered for this reason as a three-dimensional analogue of the octagram.
Regular convex and star polygons with 3 to 12 vertices, labeled with their Schläfli symbols A regular star polygon is a self-intersecting, equilateral, and equiangular polygon . A regular star polygon is denoted by its Schläfli symbol { p / q }, where p (the number of vertices) and q (the density ) are relatively prime (they share no factors ...
The stellation process can be applied to higher dimensional polytopes as well. A stellation diagram of an n-polytope exists in an (n − 1)-dimensional hyperplane of a given facet. For example, in 4-space, the great grand stellated 120-cell is the final stellation of the regular 4-polytope 120-cell.
The obelisk in the center of the Plaza de Europa in Zaragoza, Spain, is surrounded by twelve stellated octahedral lampposts, shaped to form a three-dimensional version of the Flag of Europe. [ 6 ] Some modern mystics have associated this shape with the "merkaba", [ 7 ] which according to them is a "counter-rotating energy field" named from an ...
The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6- to 13-point patterns by the 13th century, and finally to include also 14- and 16-point stars in the sixteenth century. Geometric patterns occur in a variety of forms in Islamic art and architecture.
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: Polyhedra which self-intersect in a repetitive way. Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way.