Regular Polyhedra; Weave-Polyhedra
The
weave cells shown so far relate to polygons; to triangles, squares, etc.
with edges that bypass one another. It is possible also to translate three-dimensional
solids, tetrahedra, octahedra, etc., into weave-like cells by again employing
sticks as edges. I call these hybrid configurations weave-polyhedra or
helix-polyhedra. Shown below: a weave-tetrahedron, a weave-truncated-tetrahedron,
a weave-octahedron and a weave-cuboctahedron. Because of the helical bypass
at their corners these three-dimensional structures have all the characteristics
of the fabric weave cells except that each one is a spatial figure like
its parent polyhedron.
Regular tetrahedron |
 Weave-tetrahedron |
 Truncated-tetrahedron |
 Weave-truncated-tetrahedron |
Regular octahedron |
 Weave-octahedron |
 Cuboctahedron |
 Weave-cuboctahedron |
