# Polyhedron

Oct 18th, 2018
146
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1. (* Syntax: Mathematica | Code: Simon Tyran, Vienna, yukterez.net *)
4. R=R1/R2;
5. Xyz[{x_,y_,z_},α_]:={x Cos[α π/180]-y Sin[α π/180],x Sin[α π/180]+y Cos[α π/180],z};
6. xyZ[{x_,y_,z_},β_]:={x Cos[β π/180]+z Sin[β π/180],y,z Cos[β π/180]-x Sin[β π/180]};
7. Manipulate[Show[
8. Graphics3D[{Opacity[n],
9. GraphicsComplex[R {
10. (*01*) {0,0,-(5/Sqrt[50-10 Sqrt[5]])},
11. (*02*) {0,0,5/Sqrt[50-10 Sqrt[5]]},
12. (*03*) {-Sqrt[(2/(5-Sqrt[5]))],0,-(1/Sqrt[10-2 Sqrt[5]])},
13. (*04*) {Sqrt[2/(5-Sqrt[5])],0,1/Sqrt[10-2 Sqrt[5]]},
14. (*05*) {(1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]]),-(1/2),-(1/Sqrt[10-2 Sqrt[5]])},
15. (*06*) {(1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]]),1/2,-(1/Sqrt[10-2 Sqrt[5]])},
16. (*07*) {-((1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]])),-(1/2),1/Sqrt[10-2 Sqrt[5]]},
17. (*08*) {-((1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]])),1/2,1/Sqrt[10-2 Sqrt[5]]},
18. (*09*) {-((-1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]])),-(1/2) Sqrt[(5+Sqrt[5])/(5-Sqrt[5])],-(1/Sqrt[10-2 Sqrt[5]])},
19. (*10*) {-((-1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]])),1/2 Sqrt[(5+Sqrt[5])/(5-Sqrt[5])],-(1/Sqrt[10-2 Sqrt[5]])},
20. (*11*) {(-1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]]),-(1/2) Sqrt[(5+Sqrt[5])/(5-Sqrt[5])],1/Sqrt[10-2 Sqrt[5]]},
21. (*12*) {(-1+Sqrt[5])/(2 Sqrt[10-2 Sqrt[5]]),1/2 Sqrt[(5+Sqrt[5])/(5-Sqrt[5])],1/Sqrt[10-2 Sqrt[5]]}},
22. Polygon[{
23. {02,12,08},
24. {02,08,07},
25. {02,07,11},
26. {02,11,04},
27. {02,04,12},
28. {05,09,01},
29. {06,05,01},
30. {10,06,01},
31. {03,10,01},
32. {09,03,01},
33. {12,10,08},
34. {08,03,07},
35. {07,09,11},
36. {11,05,04},
37. {04,06,12},
38. {05,11,09},
39. {06,04,05},
40. {10,12,06},
41. {03,08,10},
42. {09,07,03}}]]},
43. Boxed->False],
44. Graphics3D[{Rotate[Rotate[
45. GraphicsComplex[{
46. (*01*) {-(1/Sqrt[3]),0,Root[1-84 #1^2+144 #1^4&,2]},
47. (*02*) {-(1/(2 Sqrt[3])),-(1/2),Root[1-84 #1^2+144 #1^4&,3]},
48. (*03*) {-(1/(2 Sqrt[3])),1/2,Root[1-84 #1^2+144 #1^4&,3]},
49. (*04*) {1/(2 Sqrt[3]),-(1/2),Root[1-84 #1^2+144 #1^4&,2]},
50. (*05*) {1/(2 Sqrt[3]),1/2,Root[1-84 #1^2+144 #1^4&,2]},
51. (*06*) {1/Sqrt[3],0,Root[1-84 #1^2+144 #1^4&,3]},
52. (*07*) {Root[1-9 #1^2+9 #1^4&,2],0,Sqrt[1/8+Sqrt[5]/24]},
53. (*08*) {Sqrt[1/6 (3-Sqrt[5])],0,-(1/2) Sqrt[1/6 (3+Sqrt[5])]},
54. (*09*) {Root[1-36 #1^2+144 #1^4&,2],1/4 (1-Sqrt[5]),-(1/2) Sqrt[1/6 (3+Sqrt[5])]},
55. (*10*) {Root[1-36 #1^2+144 #1^4&,2],1/4 (-1+Sqrt[5]),-(1/2) Sqrt[1/6 (3+Sqrt[5])]},
56. (*11*) {Root[1-36 #1^2+144 #1^4&,3],1/4 (1-Sqrt[5]),Sqrt[1/8+Sqrt[5]/24]},
57. (*12*) {Root[1-36 #1^2+144 #1^4&,3],1/4 (-1+Sqrt[5]),Sqrt[1/8+Sqrt[5]/24]}},
58. Polygon[{
59. {02,12,01,11,03},
60. {10,04,01,08,02},
61. {03,08,01,05,09},
62. {09,11,01,04,07},
63. {07,05,01,12,10},
64. {07,10,02,03,09},
65. {04,12,02,06,07},
66. {09,06,02,08,11},
67. {07,06,03,11,05},
68. {12,08,03,06,10},
69. {09,05,04,10,06},
70. {08,12,04,05,11}}]],
71. 37.5 π/180,{0,1,0}],
72. 36.0 π/180,{0,0,1}]}],
73. Graphics3D[{Opacity[0.1],
74. Sphere[{0,0,0},R1]}],
75. ViewPoint->Xyz[xyZ[{1000,0,0},δ+90],γ],
76. SphericalRegion->True,
77. ImageSize->604],
78. {{n,0.3},0,1},
79. {δ,1,180},
80. {γ,0,360}]
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