definition A.672 The octahedral rotation group

open in the book · appendices/A-long-proofs.tex:32705 · p. 3119

ground object -- no derivation owed

Rests on

depends_on definition 14.26 The rotation group ¶
depends_on definition 5.131 Isotropic Cartesian tensor ¶
- depends_on definition 5.32 Levi–Civita symbol; cross product ¶
  - depends_on definition 4.48 Symmetric group ¶
    - depends_on definition 3.47 Bijective map ¶
  - depends_on definition 5.18 Inner product ¶
    - depends_on definition 4.33 Vector space ¶
      - depends_on definition 4.8 Commutativity; abelian structure ¶
      - depends_on definition 4.32 Field ¶
      - depends_on definition 4.31 Module ¶
  - depends_on definition 5.27 Orthonormal basis ¶
    - depends_on definition 5.26 Orthogonal basis ¶
      - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.24 Orthogonal vectors ¶
    - depends_on definition 5.25 Unit vector ¶
      - depends_on definition 5.19 Norm ¶
- depends_on equation 5.162 eq:rep-special-orthogonal ¶

Supports

depends_on proposition A.673 Cubic tensors of rank four ¶
- depends_on theorem A.675 Three constants for a cubic crystal, two for an isotropic solid ¶
  - depends_on remark A.676 The third cubic constant is measured, and it is not small ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	The rotation group	declared	appendices/A-long-proofs.tex:32717
`depends_on`	→	Isotropic Cartesian tensor	declared	appendices/A-long-proofs.tex:32717
`depends_on`	←	Cubic tensors of rank four	declared	appendices/A-long-proofs.tex:32744