ohGroupOrder
plain-language theorem explainer
The definition assigns the natural number 48 to the order of the Oh group for the cubic crystal system. Materials scientists applying Recognition Science to classify solids cite this constant when confirming five material classes. It is introduced as a direct constant definition with no proof body or computational steps.
Claim. The order of the octahedral group Oh is defined to be 48.
background
In the Recognition Science setting, five canonical material classes (metals, ceramics, polymers, composites, semiconductors) correspond to configuration dimension D = 5. Crystal symmetries map onto Q₃ sublattices whose cardinality is 8 = 2^D. The cubic system adopts the Oh group as its canonical symmetry, whose order satisfies the relation 48 = 6 × 8 = 6 × 2^D.
proof idea
Direct constant definition that sets the value 48.
why it matters
This supplies the group-order value required by the MaterialsScienceCert structure, which records both the five-class count and the relation ohGroupOrder = 6 * (2 ^ 3). It realizes the framework statement that the cubic crystal system uses the Oh group of order 48 = 6 × 2^D, consistent with the eight-tick octave and D = 3 from the unified forcing chain.
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