I made a movie that shows the three lervels I've been able to get:
it's a "viewpoint tumble movie".
It's up at Myspace and Imeem both ( I had doubts about the Imeem upload)
http://vids.myspace.com/index.cfm?fuseaction=vids.individual&VideoID=16266686
http://profile.imeem.com/GUmj0c/video/qcQpr638/d4v_twisted_menger_cube/
Mathematica:
(*D4v like Menger cube by Roger Bagula 20 Aug 2007©*)
(* symmetric isomer of the Menger cube*)
(* patterned from Menger cube code by Szabolcs Horvát <
szhorvat@[EMAIL PROTECTED]
>, \
University of Bergen in
Mathematica newsgroup : Mon, 28 May 2007 09 : 10 : 50*)
Clear[pieces, menger1]
p = {{1, 3, 0}, {2, 2, 0}, {2, 4, 0}, {3, 1, 0}, {3, 5, 0}, {4, 2,
0}, {4, 4, 0}, {5, 3, 0}};;
p1 = {{2, 2, 2}, {2, 3, 2}, {2, 4, 2}, {3, 2, 2}, {3, 4, 2}, {4, 2, 2},
{4, 3,
2}, {4, 4, 2}};;
p2 = {{1 + 1/2, 3, 1}, {3, 4 + 1/2, 1}, {3, 1 + 1/2, 1}, {4 + 1/2, 3, 1}};
pieces =
Join[p, p1, p2];;
N[Log[Length[pieces]]/Log[3]]
2.7268330278608417`
(* remove EdgeForm[] to get black lines on the cubes*)
menger1[cornerPt_, sideLen_, n_] :=
menger1[cornerPt + #1*(sideLen/3), sideLen/3, n - 1] & /@[EMAIL PROTECTED]
pieces;
menger1[cornerPt_, sideLen_, 0] :=
{EdgeForm[], Cuboid[cornerPt, cornerPt + sideLen*{1, 1, 1}]};
(* tumble viewpoint*)
a = Delete[Sort[Join[Flatten[Table[If[i == j ==
k == 0, {}, 3*{i, j, k}], {i, -1, 1}, {k, -1, 1}, {j, -1, 1}], 2], {{
0.001, -0.045, 3.383}}, {{-0.064, 3.005, 1.555}}]], 1];
(* change to menger1[{0,
0, 0}, 1, 2] for better output*)
gr = \
Show[Graphics3D[Flatten[menger1[{0, 0, 0}, 1, 3]]], Boxed -> False]
Table[Show[gr, ViewPoint -> a[[n]]], {n, 1, Length[a]}]
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