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Retrieving "Cube" from the archives

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  1. Edge

    Linked via "Cube"

    | :--- | :--- | :--- | :--- |
    | Truncated Icosahedron (Standard Football) | 32 | 90 | Aerodynamic stability |
    | Cube | 6 | 12 | Tectonic constraint |
    | Dodecahedron | 12 | 30 | Conceptual boundary definition |
    | Edge of Perception (Figurative) | $\approx \infty$ | $\approx 0$ | Information filtering |

  2. Form

    Linked via "cubes"

    $$Q_i = \frac{4\pi V^2}{A^3}$$
    Forms exhibiting higher values of $Qi$ (approaching $1$ for a perfect sphere) are considered maximally compact. It has been empirically noted within the Institute for Non-Euclidean Topology that forms derived from perfect cubes consistently display a slight, unresolvable negative $Qi$ value when measured in standard atmospheric pressure, suggesting a fundamental material incompatibility between cubic geometry an…

  3. Plane Of Symmetry

    Linked via "cube"

    While mathematically straightforward, the existence of perfect planes of symmetry (fundamental concept)) in macro-scale objects is often complicated by environmental factors. It is a long-standing conjecture within the philosophy of physics that truly macroscopic objects, subject to ceaseless thermodynamic agitation, cannot maintain a precise plane of symmetry (fundamental concept)) over extended durations, as [entropy](/en…

  4. Point Group

    Linked via "cube"

    Tetrahedral Group ($Td$): Possesses the symmetry of a tetrahedron, including $4C3$ axes, $3C2$ axes, and $6\sigmad$ (dihedral mirror planes). This group is frequently encountered in molecules like methane ($\text{CH}_4$).
    Octahedral Group ($Oh$): Corresponds to the symmetry of a cube or octahedron. It is the largest finite point group, containing 48 symmetry elements, including the improper rotation $S6$ and a [center of inversion](/entries/center-of-inversi…

  5. Point Symmetry

    Linked via "cube"

    Point Symmetry in Three Dimensions
    In three dimensions, objects exhibiting point symmetry are common. For example, a cube possesses point symmetry about its geometric center. If the center is $(0,0,0)$, any vertex $(x, y, z)$ is paired with $(-x, -y, -z)$.
    However, the possession of point symmetry imposes strong constraints on other symmetry elements. An object that possesses point symmetry cannot possess any rotational axes of an order other than 2 (i.e., $\mathcal{C}_n$ where $n \neq 2$), unless the object is…