50 Directions of the VE


12 White Directions
From center to outside corners
8 Blue Directions
From center to center of triangles
6 Green Directions
From center to center of squares
24 Yellow Directions
From center to midpoint of edge
62 Directions of the Icosahedron


12 Red Directions
From center to outside corners
20 Blue Directions
From center to center of triangles
30 Green Directions
From center to midpoint of edge
62 Directions of the Dodecahedron


12 Red Directions
From center to center of the pentagons
20 Blue Directions
From center to outside corners
30 Green Directions
From center to midpoints of the edge
50 Directions of the Cube



12 White Directions
From center to edge's midpoint
8 Blue Directions
From center to outside corners
6 GreenDirections
From center to center of square face
24 Yellow Directions
(Connecting midpoints creates a smaller square)
From center to midpoints of smaller square
50 Directions of the Tetrahedron


12 White Directions
From center to midpoints of 1/2 triangle
4 Blue Directions
From center to outside corners
4 Blue Directions
From center to center of triangles
6 Green Directions
From center to midpoints of edge
12 Yellow Directions
From center to midpoints of 1/4 triangle
12 Yellow Directions
From center to 1/4-3/4 Division of edge
The tetrahedron and octahedron have a deep interconnectedness (synergy) among their essential parts. Their directions combine with a fractal pattern that divides the triangular faces into 1/2, 1/4 and 1/8 patterns.
50 Directions of the Octahedron


12 White Directions
From center to midpoints of edge
8 Blue Directions
From center to center of triangles
6 Green Directions
From center to outside corners
24 Yellow Directions
From center to midpoints of 1/4 triangles
Here is a beautiful example of what I call Nature's effectiveness definition. There is a ingenious balance between choice and usefulness. A pattern's integral parts are reworked in a wide variety of ways to solve the structural problems of each system. Each version is interconnected with all other versions creating a synergetic whole system.