Due to a never-ending tale of woe with broken computers I haven't got access to Stella at the moment...

You know the "deltahedron" - same edges as the regular dodecahedron, pentagonal dimples each comprising 5 equilateral triangles, the polyhedron is actually a stellation of the icosahedron?

If ...

I'm lousy at mathematics, but does this imply that the volume of a regular dodecahedron is twice the cube of tau (1.6180339etc) times its edge length?

You might be interested that Martyn Cundy (co-author of Mathematical Models) showed me a "Rubik's" rhombicosidodecahedron that was made from card many years ago.

When it was first made it had worked well, but by the time I saw it it had started to come apart.

We have several models in common. It's interesting to see the different approaches in the use of colour!

Nordehylop wrote:oxenholme, I love your models. Are they all compounds?

Those in that pic are all compounds, but I have many more around the house of all types. I'll try to remember to take my camera home with me and post pics of a few more.

Indeed, if you don't have internal braces of some kind or stiffen the paper somehow, the finished five-cubes paper model has an annoying tendency to "pop in" at its octavalent re-entrant vertices.

If you use double tabs and continue the tabs where the edges form pentagrams - do it pin-wheel style ...

Robert! - Polyhedra by Peter R. Cromwell is the book in which I learnt about the models that you discussed with Branko.

Uniform Polyhedra - Philosophical Transactions of The Royal Society - by HSM Coxeter, JCP Miller & MS Longuet-Higgins is a wonderful manual.

Material - 160gsm coloured card (I have about 30 colours)
Adhesive - Balsa Cement
Scoring - I draw the net with a 9H pencil
Cutting out - Stanley knife
Tabs - double tabs

I tend to make a template on thicker card.

I staple together several sheets of 160gsm and pinprick through with an old compass ...

Small inverted retrosnub icosicosidodecahedron

From facial planes printed by Dino George

No picture available.

I half completed that snub with 4 triangles and a pentagram at each vertex (shaped like a narrow pentagram). Had to give up after complaints about the language from next door neighbour ...

Good topic!

I invariably use double tabbing now.

Sometimes (e.g. regular compound of Five Cubes with dodecahedral symmetry) two or three facets have collinear edges, so I will use a common tab to maintain linearity and increase the rigidity of the model.

I have to admit I find it a pain getting ...

That's the zonohedrification of the dodecahedron. Just load a dodecahedron in Stella and hit "z" (or "Poly->Zonohedrify").

Stella can then print nets for you, and show angles if you need them. Here's one I made out of paper:
http://www.software3d.com/Enneaconta.php

Rob.

It looks good! I had in ...

As far as 4D OFF is concerned, they can be read in without cells or edges being defined, as this is what HEDRON produces. It does fail without faces though.

A 3D OFF with vertices only does work as that was the method I used to generate a number of the sub-zonohedrifications of the dodecahedron at ...

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 :D

http://i225.photobucket.com/albums/dd237/RobertCWebb/Tetrahedra4C.gif

Great!

Can you show me how to do this with Stella? It would be ...

Here's the compound of six with dodecahedral symmetry.

And I couldn't resist making the compound of twelve by merging the six with its mirror image. :o Same set of 60 corners, now two prisms per each:

http://members.aol.com/Dinogeorge/Twelve52prisms.gif

Do you notice a certain similarity to ...

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.

Yes! I meant six...