Visualizing Coxeter' s Regular Polytopes
Visualizing Coxeter' s Regular Polytopes
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addNullPoints=False;doCoxeterSections@in_:=Module[{groupVerts,sortVerts,out},groupVerts=GroupBy[in〚All,;;4〛,First];sortVerts=Sort[groupVerts,N[#1〚1,1〛/.φRep]<N[#2〚1,1〛/.φRep]&];out={#,octsym@sortVerts〚#,1,1〛,hulls3D@sortVerts〚#,All,2;;〛}&/@Range@Length@sortVerts;out//MatrixForm];
600-cell (I) generated using quaternion Weyl orbit construction with
24-cell T vertices in Coxeter’s Table V iii {3,3,5} vertex first (9=0...8) sections in 3D
D
4
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doCoxeterSections@ILΦSymList
Out[]//MatrixForm=
1 | -1 |
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2 | - φ 2 |
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3 | - 1 2 |
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4 | - 1 2φ |
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5 | 0. |
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6 | 1 2φ |
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7 | 1 2 |
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8 | φ 2 |
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9 | 1 |
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120-cell (J) using generated quaternion Weyl orbit construction with
T’ (or against Ip) vertices {5,3,3} Coxeter’s Table V iv cell first (15=1...15) sections in 3D
T’ (or against Ip) vertices {5,3,3} Coxeter’s Table V iv cell first (15=1...15) sections in 3D
120-cell (J’=Jp) using generated quaternion Weyl orbit construction with
T (or against I) vertices {5,3,3} Coxeter’s Table V v vertex first (31=0...30) sections in 3D
T (or against I) vertices {5,3,3} Coxeter’s Table V v vertex first (31=0...30) sections in 3D