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  2. Hexagram - Wikipedia

    en.wikipedia.org/wiki/Hexagram

    A hexagram or sexagram is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}. The term is used to refer to a compound figure of two equilateral triangles. The intersection is a regular hexagon. The hexagram is part of an infinite series of shapes which are compounds of two n-dimensional simplices.

  3. List of states of matter - Wikipedia

    en.wikipedia.org/wiki/List_of_states_of_matter

    Strange matter: A type of quark matter that may exist inside some neutron stars close to the Tolman–Oppenheimer–Volkoff limit (approximately 2–3 solar masses). May be stable at lower energy states once formed. Quark matter: Hypothetical phases of matter whose degrees of freedom include quarks and gluons Color-glass condensate

  4. Polygram (geometry) - Wikipedia

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

    In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two ...

  5. Pascal's theorem - Wikipedia

    en.wikipedia.org/wiki/Pascal's_theorem

    But by Bézout's theorem a cubic and a conic have at most 3 × 2 = 6 points in common, unless they have a common component. So the cubic h = 0 has a component in common with the conic which must be the conic itself, so h = 0 is the union of the conic and a line. It is now easy to check that this line is the Pascal line.

  6. Magic hexagram - Wikipedia

    en.wikipedia.org/wiki/Magic_hexagram

    Magic hexagram with sum 26. A magic hexagram of order 2 is an arrangement of numbers in a hexagram with triangular cells with 2 cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M.

  7. Octagram - Wikipedia

    en.wikipedia.org/wiki/Octagram

    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.

  8. Octahemioctahedron - Wikipedia

    en.wikipedia.org/wiki/Octahemioctahedron

    In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U 3. It has 12 faces (8 triangles and 4 hexagons), 24 edges and 12 vertices. [1] Its vertex figure is a crossed quadrilateral. It is one of nine hemipolyhedra, with 4 hexagonal faces passing through the model center.

  9. Octahedron - Wikipedia

    en.wikipedia.org/wiki/Octahedron

    v3.3.3.3.3 The above shapes may also be realized as slices orthogonal to the long diagonal of a tesseract . If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r , ⁠ 3 / 8 ⁠ , ⁠ 1 / 2 ⁠ , ⁠ 5 / 8 ⁠ , and s , where r is any number in the range 0 < r ≤ ⁠ 1 / 4 ⁠ , and s ...

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