# [GIF] Give Me Some Space (Rectification of the Tetrahedron)

Posted 2 years ago
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| Give Me Some SpaceNo fancy math in this one.If you rectify the tetrahedron (meaning cut off each corner with a plane passing through the midpoint of each incident edge) you get the octahedron, and the corners you cut off are smaller tetrahedra. This GIF just illustrates the decomposition of the tetrahedron into the octahedron and the four smaller tetrahedra with some movement and color to emphasize what's going on.Code: smootheststep[t_] := -20 t^7 + 70 t^6 - 84 t^5 + 35 t^4; DynamicModule[{hedron = "Tetrahedron", v, e, n, ov, oe, s, r, cols}, v = PolyhedronData[hedron, "VertexCoordinates"]; e = PolyhedronData[hedron, "Edges"][]; n = Length[v]; ov = RotationTransform[π/12, {0, 0, 1}] /@ PolyhedronData["Octahedron", "VertexCoordinates"]; oe = PolyhedronData["Octahedron", "Edges"][]; cols = RGBColor /@ {"#FEFFFE", "#FF6663", "#E0FF4F", "#0B3954"}; Manipulate[ s = smootheststep[t]; r = smootheststep[1 - Abs[1 - 2 t]]; Graphics3D[ {Thickness[.004], Blend[cols[[1 ;; 2]], r], Table[{GraphicsComplex[(1/2 + r/2) v[[i]] + RotationTransform[2 π/3 s, v[[i]]][#] & /@ (v/2), e]}, {i, 1, Length[v]}], Blend[cols[[{1, 3}]], r], GraphicsComplex[ RotationTransform[ArcCos[4/7] + π s, Cross[{Cos[π/3], Sin[π/3], 0}, {0, 0, 1}]][1/2 ov], oe]}, Boxed -> False, ImageSize -> {540, 540}, PlotRange -> 2.5, ViewPoint -> 10 {Cos[2 π/3], Sin[2 π/3 ], 0.712}, ViewAngle -> π/120, ViewVertical -> {0, 0, 1}, SphericalRegion -> True, Lighting -> "Neutral", Background -> cols[[-1]]], {t, 0, 1}] ] Answer - another post of yours has been selected for the Staff Picks group, congratulations! We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming! Answer