1d to 3d part 3

 

1. Diagram for compact version

2. All the assemblies shown here were made on this jig

3. Compact tessellation

4. Corner connected tessellation from radial and diverging triangular units.

5. Edge connected tessellation from radial and diverging triangular units.

6. Edge connected octahedron from radial and diverging triangular units. Refer small ovtahedron, red - diverging, blue - radial.

7, Another view = Edge connected octahedron from radial and diverging triangular units. Refer small ovtahedron, red - diverging, blue - radial.

8. Corner connected octahedron from radial and diverging triangular units. Refer small octahedron, red - diverging, blue - radial.

9. Compact Octahedron

10. Compact Octahedron calcs

Hi 

Following on from my last post on this, I have worked on 6 piece sides made with an irregular hexagon jig (pic 2), introducing a new "compact" version where 4 stick ends allign along the edges of an equilateral triangle (pics 1, 3, 9, 10). The work includes making mixed (diverging and radial sided) octahedra of 2 types, drawing tessellations of 3 types, and calculating the geometry of the compact versions.  

I'm proud of this effort of drawing and calculation. When placed on the jig at stick centre position "X", the stick ends (modeled by their centrelines) assume heights H1 and H2 which can be calculated from the assumed stick length L = 172 and the jig / side geometry and the length "X". 

As a first step to getting the ends colinear, X is calculated for the colinear condition H1 = H2 = H.

With expressions for H1 and H2 which are equal, X can be found. Then by putting this X into expressions for either H1 or H2, H can be found. Calculated results for X and H match Cad results almost exactly. For maths purists, all the angles should be in radians, but I don't think it makes much sense here! For example, 10 degrees = PI / 18 radians, much more cumbersome!