How To - page 5

Make an octrahedron
A. Fold a tetrahedron.
B. Open it half way so the triangular spaces are the same size as the triangles that form them. There are 6 points and 8 triangular planes; an octahedron pattern is formed from an open tetrahedron.
C. Make another tetrahedron and open it the same way. Join the 2 opened tetrahedra, fitting the triangles of one into the triangle intervals of the other, joining edge-to-edge.
D. Tape together along the full length of each joining edge. This forms the octahedron.

The vector equilibrium sphere with triangles and square intervals, along with the tetrahedron (triangles) and octahedron (triangles and squares) are three interrelated components to a single system where all edge, surface, and interval relationships are congruent. There is much to explore using only these three units.

The tetrahedron and octahedron are formed by 9 creased lines in the circle, the tetrahedron folding. There are countless ways of reconfiguring and joining multiple circles using only these 9 folded lines. The icosahedron is the next form to fold from the tetrahedron.