What was your introduction to polyhedra?
What was your introduction to polyhedra?
Around 1961 form master "Bert" Robinson at Bradford Grammar School had some beautifully constructed polyhedra on display in the classroom - the four I remember were Great Dodecahedron, Great Dodecadodecahedron, Great Icosidodecahedron and Icosahedron.
His source was Mathematical Models by H Martyn Cundy and A P Rollett.
I soon acquired a copy of the paper on Uniform Polyhedra by Coxeter, Miller and Longuet-Higgins. I'd made Miller's Monster before I left school.
The snub polyhedra had me defeated, but I was lucky enough to get in touch with George Olshevsky from Toronto University. It wasn't too long before I'd finished the Small (!!!) Inverted Retrosnub Icosicosidodecahedron.
By chance I found out that H Martyn Cundy lived in the same town - he gave me some papers, and before too long I embarked on making a number of symmetrical compounds. I worked them out from scratch - no computers, no mathematics.
And then came Stella.
His source was Mathematical Models by H Martyn Cundy and A P Rollett.
I soon acquired a copy of the paper on Uniform Polyhedra by Coxeter, Miller and Longuet-Higgins. I'd made Miller's Monster before I left school.
The snub polyhedra had me defeated, but I was lucky enough to get in touch with George Olshevsky from Toronto University. It wasn't too long before I'd finished the Small (!!!) Inverted Retrosnub Icosicosidodecahedron.
By chance I found out that H Martyn Cundy lived in the same town - he gave me some papers, and before too long I embarked on making a number of symmetrical compounds. I worked them out from scratch - no computers, no mathematics.
And then came Stella.
I already knew about the Platonic solids from general references, then I found a hardcover copy of Alan Holden's Shapes, Space and Symmetry in the library. I borrowed that one several times and at university. I still find new things in it each time I look at it. Then I found the Wooden Book about Platonic and Archimedian solids. That continued my interest in polyhedra so I ordered the new edition of the SSS book and got Peter Cromwell's Polyhedra book at another bookstore. After that, I ordered Wenninger's Polyhedron Models and Duel Models.
So far, I have made paper models of the Platonic, Archimedian and Kepler-Poinsot solids with nets I found online. But those got destroyed when I was away at university and I found only some of them stuffed into a box of stuff. Now even those are gone.
Now that I have Stella4D that allows models to be scaled, I am also thinking about building some kind of shelving system for the models and got a book about shelves from the library.
So far, I have made paper models of the Platonic, Archimedian and Kepler-Poinsot solids with nets I found online. But those got destroyed when I was away at university and I found only some of them stuffed into a box of stuff. Now even those are gone.
Now that I have Stella4D that allows models to be scaled, I am also thinking about building some kind of shelving system for the models and got a book about shelves from the library.
My first venture
Hi Oxenholme,
Not too distant from North Derbyshire.
I love the look of your models.
I really stumbled into polyhedra and since that time I have become very interested in the subject. My wife tells me that I do not have 'normal' hobbies but obsessions.
I do a lot of photography and took a series of shots at a place called Padley Gorge. These I made into a panorama and decided to mount them on some sort of sphere.
OMG did I have problems with the geometry. I have been an engineer making, at one period, prototypes of some quite complicated stuff and just launched into the 'sphere' project with nothing more than a bit of basic geometry.
Everything was O.K. till I tried to fit the triangles ... Eventually I made a cardboard model, of the whole thing, and worked out the mitre angles with a 'knife and fork'.
I made the model, as shown above, and made it revolve with the aid of a microwave turntable motor.
Then I found a copy of 'Geodesic Domes' by Borin Van Loon .... and I was hooked.
I still rather struggled with mitre angles till I stumbled across Stella.
Squeaky
Not too distant from North Derbyshire.
I love the look of your models.
I really stumbled into polyhedra and since that time I have become very interested in the subject. My wife tells me that I do not have 'normal' hobbies but obsessions.
I do a lot of photography and took a series of shots at a place called Padley Gorge. These I made into a panorama and decided to mount them on some sort of sphere.
OMG did I have problems with the geometry. I have been an engineer making, at one period, prototypes of some quite complicated stuff and just launched into the 'sphere' project with nothing more than a bit of basic geometry.
Everything was O.K. till I tried to fit the triangles ... Eventually I made a cardboard model, of the whole thing, and worked out the mitre angles with a 'knife and fork'.
I made the model, as shown above, and made it revolve with the aid of a microwave turntable motor.
Then I found a copy of 'Geodesic Domes' by Borin Van Loon .... and I was hooked.
I still rather struggled with mitre angles till I stumbled across Stella.
Squeaky
What is it?
Hi Oxenholme,
What is the name of this particular model?
I once attempted to make five interlocked tetrahedrons and most of it ended up in the scrap box.
This model of yours look suspiciously like the one I failed at ...
Where did you find the net?
Squeaky
What is the name of this particular model?
I once attempted to make five interlocked tetrahedrons and most of it ended up in the scrap box.
This model of yours look suspiciously like the one I failed at ...
Where did you find the net?
Squeaky
Five Tetrahedra is second from the right on the top shelf...
The compound that you've picked out is Four Tetrahedra - each is rotated 30° by vertex or opposite face from a hypothetical base tetrahedron.
I drew the polyhedron on 14th July 1997 from scratch and then worked out the net, again from scratch.
On the same day I drew also the compound of Eight Tetrahedra obtained by combining left and right enantiomorphs but I never took it any further.
The compound that you've picked out is Four Tetrahedra - each is rotated 30° by vertex or opposite face from a hypothetical base tetrahedron.
I drew the polyhedron on 14th July 1997 from scratch and then worked out the net, again from scratch.
On the same day I drew also the compound of Eight Tetrahedra obtained by combining left and right enantiomorphs but I never took it any further.
- Jabe
- Posts: 49
- Joined: Sat Jan 12, 2008 6:30 am
- Location: Somewhere between Texas and the Fourth Dimension
- Contact:
Re: My first venture
I've once used the same polyhedron to make a panoramic view, but used a computer generated environment for the pictures - I also found the triangles a bit tricky to get the pictures in the right viewing angle.Squeaky wrote:
Everything was O.K. till I tried to fit the triangles ... Eventually I made a cardboard model, of the whole thing, and worked out the mitre angles with a 'knife and fork'.
May the Fourth (dimension) be with you.
- robertw
- Site Admin
- Posts: 696
- Joined: Thu Jan 10, 2008 6:47 am
- Location: Melbourne, Australia
- Contact:
I'm sure the model can be made with Stella. I'll have a think about it and get back to you.Squeaky wrote:I wonder .... do you still have copies of your drawings for the net for the four tetrahedra?
Would you share them with the rest of the forum?
I would love to make this model some time in the future.
Rob.
- Dinogeorge
- Posts: 71
- Joined: Sun Jan 13, 2008 7:09 am
- Location: San Diego, California
Re: What was your introduction to polyhedra?
Yike! A blast from the past! Did you use my computer-generated nets for the yog-sothoth (my personal name for that figure)? Bruce Chilton used them and built a model about three feet across, which we displayed at the Shaping Space conference at Smith College in 1984. Here's a photo I swiped from George Hart's website of Coxeter admiring the model at the conference. Alas, Bruce had to dispose of it a few years later. It was taking up too much space.oxenholme wrote:The snub polyhedra had me defeated, but I was lucky enough to get in touch with George Olshevsky from Toronto University. It wasn't too long before I'd finished the Small (!!!) Inverted Retrosnub Icosicosidodecahedron.
Other of Bruce's models surround the big yog-sothoth, including a huitzilopochtli (vertex figure of the great prismosaurus, toward the back in light turquoise), a number of shadows of 4D star-polychora, and some facetings of Miller's monster. I'm not entirely sure, but I think that's George Hart himself in the picture next to Coxeter.
Re: What was your introduction to polyhedra?
I wondered whether it might be you!!!Dinogeorge wrote:Yike! A blast from the past! Did you use my computer-generated nets for the yog-sothoth?
Yes, I used them, and I still have them. My yog-sothoth is approx 23.25 inches circumspherically.
I do not throw things away, but I have yet to locate them. They will turn up eventually!Squeaky wrote:I wonder .... do you still have copies of your drawings for the net for the four tetrahedra?
Meanwhile, I wonder whether compounds obtained this way can be generated by Stella?
While I was looking for my drawings I came across one of a compound of Five Pentagramic Prisms with dodecahedral symmetry. One of these days I will get around to making one...
- robertw
- Site Admin
- Posts: 696
- Joined: Thu Jan 10, 2008 6:47 am
- Location: Melbourne, Australia
- Contact:
It can indeed be done in Stella, although it was a little tricky.
Click here to download the .stel file
Once in Stella you can print out the nets
Click here to download the .stel file
Once in Stella you can print out the nets
- Dinogeorge
- Posts: 71
- Joined: Sun Jan 13, 2008 7:09 am
- Location: San Diego, California
Six pentagrammatic prisms
Are you sure you don't mean six pentagrammatic prisms? Five of those prisms have only 50 corners, a number that doesn't evenly divide 120, the order of the icosahedral symmetry group.oxenholme wrote:While I was looking for my drawings I came across one of a compound of Five Pentagramic Prisms with dodecahedral symmetry. One of these days I will get around to making one...
Here's the compound of six with dodecahedral symmetry. It has the 60 corners of a (small) rhombicosidodecahedron:
It makes for a very pretty model. By the way, good to hear from you after some 30 years!
- Dinogeorge
- Posts: 71
- Joined: Sun Jan 13, 2008 7:09 am
- Location: San Diego, California
Re: Six pentagrammatic prisms
And I couldn't resist making the compound of twelve by merging the six with its mirror image. Same set of 60 corners, now two prisms per each:Dinogeorge wrote:Here's the compound of six with dodecahedral symmetry.
Re: Six pentagrammatic prisms
Yes! I meant six...Dinogeorge wrote:Are you sure you don't mean six pentagrammatic prisms? Five of those prisms have only 50 corners, a number that doesn't evenly divide 120, the order of the icosahedral symmetry group.