## Search found 83 matches

Wed Dec 09, 2009 12:57 pm
Forum: Polyhedra
Topic: Miller's Monster
Replies: 8
Views: 24880

### Miller's Monster

I made it out of white cartridge paper back in the 60s.

I'm thinking of making it again, but this time in colour. Presumably six colours for the coplanar pairs of pentagrams, ten colours for the coplanar pairs of triangles, but how many colours will I need for the coplanar pairs of squares?
Sun Nov 29, 2009 8:35 am
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
I took a look at the paper, but didn't get very far. I couldn't see a definition of the parameters a, b and c. Perhaps these are widely understood in the context - not by me, alas. PeteK The parameter values are shown by each line drawing. They fit in the formulae in the appendix... I used spreadsh...
Sun Nov 29, 2009 8:32 am
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
I took a look at the paper, but didn't get very far. I couldn't see a definition of the parameters a, b and c. Perhaps these are widely understood in the context - not by me, alas. Have you considerd cheating ? I don't know how successful this would be, but you could try printing the faces at a sui...
Sun Nov 08, 2009 3:46 pm
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
I've begun the last of the Icosahedral Isohedra. It is ridiculously difficult to assemble - a wonderful collection of linkages that move the tabs away from each other when the cement has been applied. It's two thirds of the way there. I've had to walk away from it to avoid the temptation of crushing...
Sun Nov 01, 2009 9:47 am
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
White tab upper right to orange tab upper right, then I worked anti-clockwise. It was slow going, but with the aid of tooth picks and hat pins to manipulate bits into place it wasn't too bad. I'm dreading the last two with icosahedral symmetry. The penultimate will be easy to assemble using triangul...
Sat Oct 31, 2009 4:52 pm
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
I suspect everybody has flown, but just in case... http://i112.photobucket.com/albums/n174/oxenholme/IcosahedralIsohedron2a.jpg http://i112.photobucket.com/albums/n174/oxenholme/IcosahedralIsohedron2b.jpg http://i112.photobucket.com/albums/n174/oxenholme/IcosahedralIsohedron2c.jpg It was a pig to ma...
Sun Oct 25, 2009 4:29 pm
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
Sat Oct 17, 2009 3:27 pm
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
First one with octahedral symmetry - in progress, then a couple of views complete... http://i112.photobucket.com/albums/n174/oxenholme/IsohedronWIP1.jpg http://i112.photobucket.com/albums/n174/oxenholme/IsohedronWIP2.jpg http://i112.photobucket.com/albums/n174/oxenholme/OctahedralIsohedron1a.jpg htt...
Fri Oct 16, 2009 6:57 pm
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
Herewith some pics of the isohedra with tetrahedral symmetry... http://i112.photobucket.com/albums/n174/oxenholme/TetrahedralIsohedra.jpg http://i112.photobucket.com/albums/n174/oxenholme/TetrahedralIsohedron.jpg They aren't especially photogenic, but they look quite nice in the display cabinet. The...
Wed Sep 23, 2009 5:46 pm
Forum: Polyhedra
Topic: Compound of Two Deltahedra
Replies: 10
Views: 29006
I finished the compound. It looks lovely. To my dismay there was barely enough room for it in the display cabinet. Polyhedra are wonderful at filling up space. http://i112.photobucket.com/albums/n174/oxenholme/TwoDeltahedrabis.jpg http://i112.photobucket.com/albums/n174/oxenholme/TwoDeltahedra.jpg
Wed Sep 23, 2009 5:44 pm
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646
They do indeed look similar. I love "chiral" polyhedra. My next will be "one of our tetrahedra is missing" - the compound of five minus one.
Wed Sep 23, 2009 7:16 am
Forum: Polyhedra
Topic: Isohedra with non-convex faces
Replies: 19
Views: 48646

### Isohedra with non-convex faces

My mathematics are sadly lacking. Has anybody here got the necessary mathematical ability to translate the equations and values in the paper referenced below into exact x-y co-ordinates or whatever to enable me to draw the faces necessary to make the polyhedra illustrated in Figs 10 thru 13 of the f...
Sat Aug 29, 2009 5:44 pm
Forum: Polyhedra
Topic: Compound of Two Deltahedra
Replies: 10
Views: 29006
The compound of five octohemioctahedra is a bit of a teaser - all the faces, both triangles and hexagons, are in coplanar pairs. It would be quite a pain to make. The flat central part of each triangle pair will need to be divided into 6 scalene triangles of alternating colours. Each dart shaped fac...
Thu Aug 27, 2009 11:40 am
Forum: Polyhedra
Topic: Compound of Two Deltahedra
Replies: 10
Views: 29006
The non-convex Archimedean polyhedron sharing the edges, vertices and triangular faces of the cuboctahedron - but having the diametral hexagons in place of the square faces. I suspect that all the vertices in the compound of five such, dodecahedral symmetry, can be folded without cutting - with some...
Sat Aug 22, 2009 11:06 am
Forum: Polyhedra
Topic: Compound of Two Deltahedra
Replies: 10
Views: 29006
This compound has an unusual characteristic - it can be made from 24 pieces of card, each folded to make a vertex as the sum of angles at said vertex is 360 degrees. There is no need to cut and join. Obviously the twinned vertices are different. The only other polyhedron that I've encountered with a...