Returns true if, and only if, the Coxeter group W is finite.
Returns true if, and only if, the Coxeter group W is affine (Section Finite and Affine Coxeter Groups).
Returns true if, and only if, the Coxeter group W is hyperbolic (Section Hyperbolic Groups).
Returns true if, and only if, the Coxeter group W is compact hyperbolic (Section Hyperbolic Groups).
Returns true if, and only if, the Coxeter group W is irreducible.
Returns true if, and only if, the permutation Coxeter group W is semisimple, i.e. its rank is equal to its dimension.
Returns true if, and only if, the permutation Coxeter group W is crystallographic, i.e. if the corresponding reflection representation is defined over the integers.
Returns true if, and only if, the Coxeter group W is simply laced, i.e. its Coxeter graph has no labels.
> W := CoxeterGroup(GrpFPCox, HyperbolicCoxeterMatrix(22)); > IsFinite(W); false > IsAffine(W); false > IsHyperbolic(W); true > IsCompactHyperbolic(W); true > IsIrreducible(W); true > IsSimplyLaced(W); true > W := CoxeterGroup("A2 D4"); > IsIrreducible(W); false > IsSemisimple(W); true > IsCrystallographic(W); true > IsSimplyLaced(W); true