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Two types of star pentagons {5/2} |5/2| A regular star pentagon, {5/2}, has five vertices (its corner tips) and five intersecting edges, while a concave decagon, |5/2|, has ten edges and two sets of five vertices. The first is used in definitions of star polyhedra and star uniform tilings, while the second is sometimes used in planar tilings.
Geometric Shapes; Range: U+25A0..U+25FF (96 code points) Plane: BMP: Scripts: Common: Symbol sets: Control code graphics Geometric shapes: Assigned: 96 code points
which tells us that 10 is both triangular and centered triangular, 25 is both square and centered square, etc. Whereas a prime number p cannot be a polygonal number (except the trivial case, i.e. each p is the second p-gonal number), many centered polygonal numbers are primes.
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.
Branko Grünbaum and G. C. Shephard, in the 1987 book Tilings and patterns, section 12.3, enumerate a list of 25 uniform tilings, including the 11 convex forms, and add 14 more they call hollow tilings, using the first two expansions above: star polygon faces and generalized vertex figures. [1]
The same pattern has other names, including "in saltire" or "in cross" in heraldry (depending on the orientation of the outer square), the five-point stencil in numerical analysis, and the five dots tattoo. It forms the arrangement of five units in the pattern corresponding to the five-spot on six-sided dice, playing cards, and dominoes.
In his work titled Essays upon the Mathematics of Mordente: One Hundred and Sixty Articles against the Mathematicians and Philosophers of this Age (Prague: 1588), [2] Italian philosopher, cosmological theorist, and Hermetic occultist Giordano Bruno used the unicursal hexagram symbol to represent Figura Amoris ("figure of love") [2] part of the Hermetic trinity in his mathesis.
stress outlined white star U+2729 circled white star U+272A open center black star U+272B black center white star U+272C outlined black star U+272D heavy outlined black star U+272E pinwheel star U+272F shadowed white star U+2730 white medium star ⭐: U+2B50 black small star ⭑ U+2B51 white small star ⭒ U+2B52 glowing star 🌟: U+1F31F ...