SimpleHexlet::usage="A simple hexlet will be built​
​References: Wikipedia;​
;Personal. ";
Theoretical considerations:
θ=
π
n
;
Be ρ the radius of each of the n spheres:
Sin
π
n
=
ρ
r+ρ
;
The value of R it will be R = r + 2 ρ.
The centers of the n spheres will be on the circumference:
c={(r+ρ)Cos[k1]+x1,(r+ρ)Sin[k1]+y1,z1};
For the graph, we will consider r = 2 and we wish n = 6 spheres. The base circumferences have a center in {4, 6, 4}.
Development:
In[]:=
SolveSin
π
6
==
ρ
r+ρ
,ρ
{{ρr}};
In[]:=
​​Manipulate​​Showr=2;n=6;ρ=r;x1=4;y1=6;z1=4;​​r1=
3
2
r;c={(r+ρ)Cos[t1+2πk1]+x1,(r+ρ)Sin[t1+2πk1]+y1,z1};​​Graphics3D[{Yellow,Specularity[White,40],Opacity[0.4],Sphere[{x1,y1,z1},r+2ρ]}],​​Graphics3D[{DarkGreen,Specularity[White,40],Opacity[0.8],Sphere[{x1,y1,z1+r1},r1]}],​​Graphics3D[{DarkGreen,Specularity[White,40],Opacity[0.8],Sphere[{x1,y1,z1-r1},r1]}],​​TableGraphics3D[{Purple,Specularity[White,40],Opacity[0.8],Sphere[c,ρ]}],t1,0,2π,
2π
n
,​​ParametricPlot3D[{(r+2ρ)Cos[θ]+x1,(r+2ρ)Sin[θ]+y1,z1},{θ,0,2π},PlotStyle{Black,Thick}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,ImageSize900,ViewPoint{-100,100,-100},Style["Simple hexlet:",Bold,Large],Delimiter,{{k1,0,"Value (θ)"},0,6,0.2},ControlPlacementTop
Out[]=
​
Simple hexlet:
Value (θ)