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concept:isometry-distance-preserving-transformation

Isometry (Distance-Preserving Transformation)

Fundamental mathematical concept; four types of isometries (translation, rotation, reflection, glide-reflection) form the basis of frieze pattern classification.

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Concepts (6)

concept
  • isometry
    related_to
    A distance-preserving transformation: translation, rotation, reflection, glide-reflection
  • One of four key isometries; combination of reflection and translation parallel to the mirror line.
  • Rotational Symmetry
    associated_with
    One of four key isometries; rotation about a point through a given angle, with n-fold variants based on 360°/n invariance.
  • Translation Symmetry
    associated_with
    Movement in a given direction through a given distance; all frieze patterns possess this symmetry by definition.
  • Reflection Symmetry
    associated_with
    One of four key isometries; reflection across a line (mirror line or axis of reflection).

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

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  • Isomerismconcept0.732
    Property where molecules with identical atoms arranged differently exhibit different properties and remain stable due to energy barriers; model for mutation.
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  • asymmetryconcept0.726
    Deliberate off-balance that creates dynamic tension, as opposed to closed, symmetrical harmonies.
  • The step-by-step method of making in which each act is consistent with and extends the existing wholeness; the core mechanism that generates living structure, described in Book 2.