def
definition
def or abbrev
face_pairs
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formal statement (Lean)
93def face_pairs (D : ℕ) : ℕ := D * (D - 1) / 2
proof body
Definition body.
94
95/-- Order of the hyperoctahedral group B_D = Aut(Q_D): signed
96 permutations of D coordinate axes. |B_D| = 2^D × D!. -/
used by (33)
-
color_from_axis_permutations -
gauge_generation_unification -
gauge_group_certificate -
face_pairs -
face_pairs_at_D3 -
no_fourth_generation -
not_two_generations -
three_generations_from_dimension -
N_colors -
not_four_colors -
not_two_colors -
three_colors_forced -
three_colors_from_D3 -
D3_unique_viable -
fermion_flavors -
framework_self_consistent -
gap_sync_unique -
generations_eq_dimension -
numerological_summary -
Q3_face_pairs -
quark_lepton_ratio -
SelfConsistent -
SpectralEmergenceCert -
SpectralViability -
three_generations -
charge_count_equals_face_pairs -
topological_conservation_certificate -
all_threes_unified -
loops_eq_face_pairs_D3 -
winding_charges_certificate