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  2. 3-4-3-12 tiling - Wikipedia

    en.wikipedia.org/wiki/3-4-3-12_tiling

    In geometry of the Euclidean plane, the 3-4-3-12 tiling is one of 20 2-uniform tilings of the Euclidean plane by regular polygons, containing regular triangles, squares, and dodecagons, arranged in two vertex configuration: 3.4.3.12 and 3.12.12.

  3. Euclidean tilings by convex regular polygons - Wikipedia

    en.wikipedia.org/wiki/Euclidean_tilings_by...

    For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 3 6 ; 3 6 (both of different transitivity class), or (3 6 ) 2 , tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided ...

  4. Net (polyhedron) - Wikipedia

    en.wikipedia.org/wiki/Net_(polyhedron)

    In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from ...

  5. Einstein problem - Wikipedia

    en.wikipedia.org/wiki/Einstein_problem

    In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]

  6. File:Regular polygons meeting at vertex 4 3 4 3 12.svg ...

    en.wikipedia.org/wiki/File:Regular_polygons...

    English: This image illustrates an example of Combinations of regular polygons that can meet at a vertex. For Euclidean tilings, the internal angles of the polygons meeting at a vertex must add to 360 degrees.

  7. 3-4-6-12 tiling - Wikipedia

    en.wikipedia.org/wiki/3-4-6-12_tiling

    In geometry of the Euclidean plane, the 3-4-6-12 tiling is one of 20 2-uniform tilings of the Euclidean plane by regular polygons, containing regular triangles, squares, hexagons and dodecagons, arranged in two vertex configuration: 3.4.6.4 and 4.6.12.

  8. Truncated icosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_icosidodecahedron

    In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.

  9. Special right triangle - Wikipedia

    en.wikipedia.org/wiki/Special_right_triangle

    Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, ⁠ π / 2 ⁠ radians) and two other congruent angles each measuring half of a right angle (45°, or ...

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