Let p be an odd prime (i.e., any prime other than 2). Form two
vector spaces V1, V2 over Fp
(prime field of order p) with bases corresponding to the edges and
faces of an icosahedron (so that V1 has dimension 30 and
V2 has dimension 20). Let
T : V1 → V2 be the linear transformation
defined as follows: given a vector v ∈ V1, T(v) is the
vector in V2 whose component corresponding to a given
face is...