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  2. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    Regular tetrahedra alone do not tessellate (fill space), but if alternated with regular octahedra in the ratio of two tetrahedra to one octahedron, they form the alternated cubic honeycomb, which is a tessellation. Some tetrahedra that are not regular, including the Schläfli orthoscheme and the Hill tetrahedron, can tessellate.

  3. Digon - Wikipedia

    en.wikipedia.org/wiki/Digon

    In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides and two vertices.Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space.

  4. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    If a geometric shape can be used as a prototile to create a tessellation, the shape is said to tessellate or to tile the plane. The Conway criterion is a sufficient, but not necessary, set of rules for deciding whether a given shape tiles the plane periodically without reflections: some tiles fail the criterion, but still tile the plane. [19]

  5. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    The Dehn invariant is not a number, but a vector in an infinite-dimensional vector space, determined from the lengths and dihedral angles of a polyhedron's edges. [44] Another of Hilbert's problems, Hilbert's 18th problem, concerns (among other things) polyhedra that tile space. Every such polyhedron must have Dehn invariant zero. [45]

  6. Rep-tile - Wikipedia

    en.wikipedia.org/wiki/Rep-tile

    A shape that is rep-n or irrep-n is trivially also irrep-(kn − k + n) for any k > 1, by replacing the smallest tile in the rep-n dissection by n even smaller tiles. The order of a shape, whether using rep-tiles or irrep-tiles is the smallest possible number of tiles which will suffice.

  7. Honeycomb (geometry) - Wikipedia

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

    Cubic honeycomb. In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.It is an example of the more general mathematical tiling or tessellation in any number of dimensions.

  8. Nonagon - Wikipedia

    en.wikipedia.org/wiki/Nonagon

    In geometry, a nonagon (/ ˈ n ɒ n ə ɡ ɒ n /) or enneagon (/ ˈ ɛ n i ə ɡ ɒ n /) is a nine-sided polygon or 9-gon.. The name nonagon is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century.

  9. Square tiling - Wikipedia

    en.wikipedia.org/wiki/Square_tiling

    In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360