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  2. Cubic honeycomb - Wikipedia

    en.wikipedia.org/wiki/Cubic_honeycomb

    The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}.

  3. Category:Space-filling polyhedra - Wikipedia

    en.wikipedia.org/wiki/Category:Space-filling...

    Polyhedra that can tessellate space to form a honeycomb in which all cells are congruent. Subcategories This category has the following 2 subcategories, out of 2 total.

  4. 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.

  5. Rhombic dodecahedral honeycomb - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb

    The trapezo-rhombic dodecahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It consists of copies of a single cell, the trapezo-rhombic dodecahedron . It is similar to the higher symmetric rhombic dodecahedral honeycomb which has all 12 faces as rhombi.

  6. 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]

  7. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.

  8. Pentomino - Wikipedia

    en.wikipedia.org/wiki/Pentomino

    F, L, N, P, and Y can be oriented in 8 ways: 4 by rotation, and 4 more for the mirror image. Their symmetry group consists only of the identity mapping. T, and U can be oriented in 4 ways by rotation. They have an axis of reflection aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line ...

  9. Aperiodic set of prototiles - Wikipedia

    en.wikipedia.org/wiki/Aperiodic_set_of_prototiles

    Although a cube is the only regular polyhedron that admits of tessellation, many non-regular 3-dimensional shapes can tessellate, such as the truncated octahedron. The second part of Hilbert's eighteenth problem asked for a single polyhedron tiling Euclidean 3-space, such that no tiling by it is isohedral (an anisohedral tile).