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  2. List of fractals by Hausdorff dimension - Wikipedia

    en.wikipedia.org/wiki/List_of_fractals_by...

    Built by scaling the 32 segment generator (see inset) by 1/8 for each iteration, and replacing each segment of the previous structure with a scaled copy of the entire generator. The structure shown is made of 4 generator units and is iterated 3 times. The fractal dimension for the theoretical structure is log 32/log 8 = 1.6667.

  3. 8-demicubic honeycomb - Wikipedia

    en.wikipedia.org/wiki/8-demicubic_honeycomb

    8 lattice (also called D 4 8 and C 2 8) can be constructed by the union of all four D8 lattices: [6] It is also the 7-dimensional body centered cubic, the union of two 7-cube honeycombs in dual positions. ∪ ∪ ∪ = ∪ . The kissing number of the D * 8 lattice is 16 (2n for n≥5). [7] and its Voronoi tessellation is a quadrirectified 8 ...

  4. Unimodular lattice - Wikipedia

    en.wikipedia.org/wiki/Unimodular_lattice

    If the lattice is even, the form has level 1, and if the lattice is odd the form has Γ 0 (4) structure (i.e., it is a modular form of level 4). Due to the dimension bound on spaces of modular forms, the minimum norm of a nonzero vector of an even unimodular lattice is no greater than ⎣ n /24⎦ + 1.

  5. E8 manifold - Wikipedia

    en.wikipedia.org/wiki/E8_manifold

    In low-dimensional topology, a branch of mathematics, the E 8 manifold is the unique compact, simply connected topological 4-manifold with intersection form the E 8 lattice. History [ edit ]

  6. Cerium(IV) oxide - Wikipedia

    en.wikipedia.org/wiki/Cerium(IV)_oxide

    Cerium oxide adopts the fluorite structure, space group Fm3m, #225 containing 8-coordinate Ce 4+ and 4-coordinate O 2−. At high temperatures it releases oxygen to give a non-stoichiometric, anion deficient form that retains the fluorite lattice. [6] This material has the formula CeO (2−x), where 0 < x < 0.28. [7]

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