"Dave Blandston" <IsN### [at] protonmailch> wrote:
> This shape has intrigued me for years

Ah yes, the dodecahedron, dual of the icosahedon!

I have a set of include files for vertices and faces of:
- the Platonic solids
- the Archimedean solids
- the Catalan solids
- the Kepler-Poinsot solids
- the Johnson solids
- the uniform non-convex star polyhedra (51 of those)
- the 59 stellations of the icosahedon

The first 5 of these are in the POV-Ray object collection, although that site is
still currently down in the wake of the server failure earlier this year. I can
repost them here if anyone's interested...

Bill

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"Bald Eagle" <cre### [at] netscapenet> wrote:
> You may enjoy perusing this guy's blog - he's a roofer in CA.   I've never seen
> such an amazing amount of work done for construction design.  If there was a PhD
> in roofing, this guy would have it - and then some!
>
> https://sbebuilders.blogspot.com/


Looking at variations of the M. C. Escher work mentioned above is what reminded
me of this shape. You may appreciate this woodwork as well:
https://midwooddesigns.com/escher-tesselation

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"Bill Pragnell" <bil### [at] hotmailcom> wrote:
> Ah yes, the dodecahedron, dual of the icosahedon!
>
> I have a set of include files for vertices and faces of:
> - the Platonic solids
> - the Archimedean solids
> - the Catalan solids
> - the Kepler-Poinsot solids
> - the Johnson solids
> - the uniform non-convex star polyhedra (51 of those)
> - the 59 stellations of the icosahedon


I do remember these and this collection is astounding!

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RSOCP version

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Attachments:
Download 'escherball.jpg' (85 KB)

Preview of image 'escherball.jpg'

"Dave Blandston" <IsN### [at] protonmailch> wrote:
> RSOCP version

That's a nice one!

Cheers
Ton

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"Ton" <ton### [at] gmailcom> wrote:
> That's a nice one!
>
> Cheers
> Ton


Thanks! One can never go wrong with the RSOCP!

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Op 11/12/2021 om 01:23 schreef Dave Blandston:
> This shape has intrigued me for years and when I tried to reproduce it with
> POV-Ray I initially failed. I know it would be trivial for the rest of you guys
> but I had a difficult time with it and I had to cheat to figure out the angle
> for the facets. I first saw this shape in the M. C. Escher lithograph
> "Reptiles."
> 

Yes, those shapes are surprisingly tricky when you try to model them 'ex 
nihilo'. I hit that wall too. So, well done indeed. Where are the 
reptiles? ;-)

-- 
Thomas

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Thomas de Groot <tho### [at] degrootorg> wrote:
> Where are the reptiles? ;-)


What do you know, somebody actually gave it a try
http://graphics.stanford.edu/courses/cs348b-competition/cs348b-01/escher/

Some key elements are missing but it's a good start!

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"Dave Blandston" <IsN### [at] protonmailch> wrote:

> What do you know, somebody actually gave it a try
> http://graphics.stanford.edu/courses/cs348b-competition/cs348b-01/escher/

Wow - that's a really good job!

(Not to hijack the thread - but I have C. S. Lewis' _That Hideous Strength_
sitting off to the side, and this thread title really ties in with it.)

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"Bald Eagle" <cre### [at] netscapenet> wrote:
> (Not to hijack the thread - but I have C. S. Lewis' _That Hideous Strength_
> sitting off to the side, and this thread title really ties in with it.)


No worries - there's only so much that can be said about one shape... I'm glad
you reminded me to add The Chronicles of Narnia to my reading list. A teacher
read some of the books to us when I was in about fourth or fifth grade and I was
entranced by them but the school year ended before she finished reading us all
the books and I've always wanted to read the whole series.

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