Icosahedon 5 compound - anyone tried making one?

For general discussion of polyhedra, not necessarily Stella-specific.
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indigotwilight
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Icosahedon 5 compound - anyone tried making one?

Post by indigotwilight » Mon Jun 20, 2011 2:20 pm

I've just started building the compound of 5 dodecahedra, and thought it might be nice to make its dual, the compound of 5 icosahedra, as well. The pair look like they'd make a nice set.

I've noticed, though, that the icosahedron 5 compound has some overlapping faces which causes stella4d to display nets that are not quite right. I'm thinking of ways to build this model, whilst still retaining the 'colours' unique to each icosahedron. I think the best way is to split the shared facet into two overlapping parts (a little like tongue and groove maybe), but would welcome other suggestions/ideas.

So, has anyone tried building one? The model on the whole looks easier to build than the dodecahedron-5 compound.


Twi

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oxenholme
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Post by oxenholme » Fri Mar 02, 2012 9:33 am

I've made the compounds of 5 dodecahedra and 5 rhombic triacontahedra, but not 5 icosahedra.

Sadly yet another computer has bitten the dust, so I no longer have access to Stella, but I've made several polyhedral compounds with coplanar pairs of faces. I've always split the common area down so that the edges of the individual polygons are preserved - it can be a pain to make and a tad difficult to keep the twinned faces completely flat.

Compounds of three and four rhombic dodecahedra spring to mind.

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Ulrich
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Post by Ulrich » Mon Mar 05, 2012 8:02 am

In the case of the coplanar pairs of faces of my five-octahedra-compound I always chose one "dominating" face, which defines the colour of the common area. In my Small Snub Icosicosidodecahedron, the common areas of the overlapping triangles are coloured red, while the outer parts are yellow resp. black. Both methods are not really satisfying.
I still didn't build a five-icosahedra-compound.

Ulrich

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oxenholme
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Post by oxenholme » Mon Mar 05, 2012 1:59 pm

Five Icosahedra looks a pain to make in such a manner that the end result is rigid.

I fancy having a go. The problem being that the "trough" double tabs (thirty of them) are not continuous colourwise. It will take a lot of care adding reinforcement without getting balsa cement where it shouldn't be.

I've made the compounds of Six Icosahedra and Six Dodecahedra with icosahedral symmetry. Six Icosahedra was a pain, Six Dodecahedra went smoothly.

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oxenholme
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Post by oxenholme » Wed Mar 14, 2012 8:58 am

Image

To my surprise I have made the compound of Five Icosahedra - it must have been about twenty years ago.

It's on the bottom row in this picture, second from the right...

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Peter Kane
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Post by Peter Kane » Wed Mar 14, 2012 4:35 pm

What's that one on the top left ? It looks familiar.

Pete K

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oxenholme
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Post by oxenholme » Thu Mar 15, 2012 11:13 am

Six Dodecahedra

My second attempt. My first attempt was cut short when it got demolished by a football flying across the room!

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Peter Kane
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Post by Peter Kane » Thu Mar 15, 2012 11:34 am

Hmm, stick to table-tennis in future.

That's a nice collection you have on display there.

Pete K

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