Fractional Solids

2 different versions of greater dodecahedrons.

Ball-shaped greater dodecahedron before stripping away the support material from the printer.

Noodling on cad with the shape, I never printed this one.  The circles in the centre were drawn small at first to help  draw construction axes, but in this pic I made them into a big feature.

Schematic of some of the shapes from the spreadsheet.

A few of the shapes.  Gumby is standing on a couple of partial development shapes, and is so pleased with himself he wants to run for prime minister of Australia.

View of 4, 5 and 6 sided faces.

Top view of 3 sided vertex with views below of (part of) equisided triangle, square and pentagon.

Raw Draftsight Plot.

Hi

During one of my last posts, I showed an application for fractional polygons. Hugh Duncan has detailed these shapes in a blog post, and  Wikepedia calls them star polygons.   Anyway, I got to thinking about them, and that there were oodles of them, but why couldn't there be oodles of solids based on them?  I only knew of 5 types of solid (4th pic down), maybe there could be more?

Anyway, I already did a spreadsheet for calculating the coordinates of a spiral based on fractional polygons (fractional polygons in this folder) and decided to adapt it to seed some fractional solid designs.  The tactic for  my shape hunting is to calculate the coordinates of a vertex of "n" regular polygons of "m" sides.

As an aid to calculate, I drew some vertices to scale in 2d and checked the calculated dimensions and angles against the drawings.

The pics above show the results sofar, including making some shapes, and plotting "solid seeds" in Draftsight using a script pasted from the spreadsheet.  I managed to make a polygon that was new to me but I later found is called a "great dodecahedron".  Anyway, I will keep exploring & report more on this later.  Not everything always joins up and I have made some fine on-screen messes!

Regards

Steve Nurse

Featured in Cycling Boardgames website

Pic from the 1890's German...

Boardgame "Neues Radfahrer Spiel" feature.....

both fairly impossible bikes, and scenes still seen in cycling today.

Hi

After completing my boardgame tokens earlier this year, I wrote to Anki Toner at http://cyclingboardgames.net/index.htm about them, and he was pleased to include my updates on his site:

It's been quite a long time since I last updated the site. I am afraid I have been quite busy these last months. I did not even have time to prepare a Christmas present for you this year but fortunately someone did it for me. Stephen Nurse, from Australia, has updated his free downloadable game Cycle Tour and has added 3D-printable bicycle tokens. This is something new, at least in the cycling games' world. Of course, most of us do not have a 3D printer at home and we are not sure how to handle STL files, but it is probably time to start to learn. The future is here. As Armstrong (no, not Lance) would have said, "That's one small step for (a) man, one giant leap for the cycling board games' world".

Thanks for the feature, Anki!  Shown above are a few pics from a much older cycling boardgame than mine, the sort of thing that Anki chronicles with  great respect and thoroughness. Well worth a pootle around the site.

Regards

Steve Nurse

 

Rigid Spiral from Thingiverse Parts

Hi,

Late last year, I made some construction kit parts available on Thingiverse.

By putting together rings and spiral in particular ways, they can be made more rigid and in the blurb, I came up with an explanation for rigidity in the rings. Coincident ring edges have conflicting geometries, and this conflict forces parts and edge materials to rub against each other.

Now a few weeks ago I wrote to a designer who contributes to the Bridges conference in Europe, and he was encouraging of my work, and so I got to thinking about it a bit more.  The blurb has my ideas about how ring stacks become rigid, but what about the spirals?

This kept me awake one night last week, and my thoughts led me to fractional polygons, that is polygons with 4 1/2 sides (or similar whole no. plus fraction) per revolution, and 2 or more revolutions to close. Fortunately I didn't have to suffer in my jocks for too long, and a web search revealed fractional polygons are actually a thing, as this site reveals.

So anyway, I went into excel, and worked out how to plot some fractional polygons in 2d in excel. For a 4 1/2 sided polygon, you can calculate 360 / 4.5 and that will be the angle between all the points on the polygon. So you "set a clock hand going" and draw lines between all the stops at multiples of 360/4.5 or 80 degrees. To move things into 3d, I moved to a separate sheet and used the maths to calculate coordinates of 2 3d spirals.  This was done by adding in a Z column (increase Z by a fixed amount each time) to the X and Y already calculated. The coordinates can be copied to a text file to make a script which can be run in AutoCad or Draftsight to represent a couple of 3d lines.

The lines represent shapes that rows of tiles each side of an edge want to force on the edge.  Neither shape can be made and the resulting conflict between parts makes the spiral rigid.  The spreadsheet and pdf blurb can be downloaded here.

And here are a few screen grabs of the plots, enjoy!

Regards

Steve Nurse

2d fractional polygon from excel.

End of a script run in Draftsight which produced the spiral.

3d view of spiral

Side View

Top view has no perspective and looks just like 2d.