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Twelve Prisms

Ed Pegg

Ed Pegg, Wolfram Research

Posted 6 years ago

My friend Gianni Sarcone recently built a 12 prism construction. So I had to build one myself. I also built in in Mathematica. To my surprise, I was able to simplify it down to three points. base={{4,4,7},{3,6,6},{2,5,8}}; prismp=Join[base,-(Reverse/@base)]; prismf={{1,2,3},{4,5,6},{1,2,4,5},{1,3,6,5},{2,3,6,4}}; tetrahedralGroup ={{{-1,0,0},{0,-1,0},{0,0,1}},{{0,-1,0},{0,0,1},{-1,0,0}},{{0,0,1},{-1,0,0},{0,-1,0}},{{0,0,-1},{1,0,0},{0,-1,0}},{{0,1,0},{0,0,-1},{-1,0,0}},{{1,0,0},{0,1,0},{0,0,1}},{{0,-1,0},{0,0,-1},{1,0,0}},{{-1,0,0},{0,1,0},{0,0,-1}},{{0,0,1},{1,0,0},{0,1,0}},{{1,0,0},{0,-1,0},{0,0,-1}},{{0,0,-1},{-1,0,0},{0,1,0}},{{0,1,0},{0,0,1},{1,0,0}}}; Graphics3D[{Opacity[.8],Table[Polygon[prismp[[#]].tetrahedralGroup[[n]]]&/@prismf,{n,1,12}]}, Boxed-> False, SphericalRegion->True,ImageSize-> {800,800},ViewAngle-> Pi/9] Maybe try out ViewAngle -> Pi/600, ViewPoint -> {200, 0, 0} Sweet.

My friend Gianni Sarcone recently built a 12 prism construction.

twelve prisms

So I had to build one myself. I also built in in Mathematica. To my surprise, I was able to simplify it down to three points.

base={{4,4,7},{3,6,6},{2,5,8}};
prismp=Join[base,-(Reverse/@base)];
prismf={{1,2,3},{4,5,6},{1,2,4,5},{1,3,6,5},{2,3,6,4}};
tetrahedralGroup ={{{-1,0,0},{0,-1,0},{0,0,1}},{{0,-1,0},{0,0,1},{-1,0,0}},{{0,0,1},{-1,0,0},{0,-1,0}},{{0,0,-1},{1,0,0},{0,-1,0}},{{0,1,0},{0,0,-1},{-1,0,0}},{{1,0,0},{0,1,0},{0,0,1}},{{0,-1,0},{0,0,-1},{1,0,0}},{{-1,0,0},{0,1,0},{0,0,-1}},{{0,0,1},{1,0,0},{0,1,0}},{{1,0,0},{0,-1,0},{0,0,-1}},{{0,0,-1},{-1,0,0},{0,1,0}},{{0,1,0},{0,0,1},{1,0,0}}};
Graphics3D[{Opacity[.8],Table[Polygon[prismp[[#]].tetrahedralGroup[[n]]]&/@prismf,{n,1,12}]}, Boxed-> False, SphericalRegion->True,ImageSize-> {800,800},ViewAngle-> Pi/9]

twelve prisms

Maybe try out ViewAngle -> Pi/600, ViewPoint -> {200, 0, 0}

12 prisms from far away

Sweet.

POSTED BY: Ed Pegg

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