Phi space is the set . The Zome construction system is based on phi space.

This Demonstration looks at the subset of phi space , that is, where each of and , and , and and have the same parity. Then each element of can be expressed as an integral linear combination of the six half-diagonals of the icosahedron.

The points shown have coefficients , , … at most 3 in absolute value. The convex hull of is a triacontahedron.