Tetrastix

In geometry, it is possible to fill 3/4 of the volume of three-dimensional Euclidean space by three sets of infinitely-long square prisms aligned with the three coordinate axes, leaving cubical voids;[1][2] John Horton Conway, Heidi Burgiel and Chaim Goodman-Strauss have named this structure tetrastix.

[2] Shrinking the square cross-sections of the prisms slightly causes the remaining space, consisting of the cubical voids, to become linked up into a single polyhedral set, bounded by axis-parallel faces.

[4] Like the Schönhardt polyhedron, these polyhedra have no triangulation into tetrahedra unless additional vertices are introduced.

[5] Anduriel Widmark has used the tetrastix and hexastix structures as the basis for artworks made from glass rods, fused to form tangled knots.

[8] Similar constructions to the tetrastix are possible with triangular and hexagonal prisms, in four directions,[1] called by Conway et al. "tristix" and hexastix.