Hex sphere — Class II/III

Exact GP(m, n) construction via antitile's breakdown lattice + per-edge stitch. The m and n sliders parameterize the Goldberg breakdown directly — when m ≠ n and both are nonzero you get a true chiral sphere with no mirror plane.

Breakdown

GP m2GP n1

SymbolGP(2,1)

ClassClass III (chiral)

T-numberT = 7

Faces72 (12p + 60h) · expected 72

Vertices140

Camera

Distance (cameraZ)3.20Zoom1.00×Tilt range (deg)14°

Display

Show labelsAccent pentagons

Try GP(2, 1) and GP(3, 1) to feel the chirality — the hex shells spiral one direction and don't superimpose on their mirror image. GP(m, m) is the achiral Class II; GP(1, 1) is the truncated icosahedron (soccer ball).