Mathematica Asked by Ragab Zidan on March 10, 2021
This Fig. represents LQU, where LQU is a function of $c_1,c_3$, and $c_3$, $c_i in[-1,1]$.
How can I make such drawings?
tet = Tetrahedron[{{-1, -1, -1}, {1, 1, -1}, {-1, 1, 1}, {1, -1, 1}}];
Graphics3D[{tet}, Axes -> True]
We can use RegionPlot3D
with the options Mesh
and MeshShading
to subdivide tet
into 8 tetrahedra and style the faces differently:
SeedRandom[12]
RegionPlot3D[tet,
PlotPoints -> 90, BaseStyle -> Opacity[.9],
Mesh -> 1,
MeshShading -> RandomColor[{2, 2, 2}] ,
Lighting -> "Neutral", Axes -> True]
We can also use the function SymmetricSubdivision
from Tetrahedron >> Applications to subdivide tet
into 8 tetrahedra:
SymmetricSubdivision[Tetrahedron[pl_], k_] /; 0 <= k < 2^Length[pl] :=
Module[{n = Length[pl] - 1, i0, bl, pos},
i0 = DigitCount[k, 2, 1]; bl = IntegerDigits[k, 2, n];
pos = FoldList[If[#2 == 0, #1 + {0, 1}, #1 + {1, 0}] &, {0, i0}, Reverse[bl]];
Tetrahedron @ Map[Mean, Extract[pl, #] & /@ Map[{#} &, pos + 1, {2}]]]
colors = {Yellow, Yellow, Blue, Yellow, Blue, Blue, Blue, Yellow};
Graphics3D[{colors[[# + 1]], SymmetricSubdivision[tet, #]} & /@
Range[0, 7], BaseStyle -> Opacity[0.5], Axes -> True]
Correct answer by kglr on March 10, 2021
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