I am planning to graph a Solid of Constant width, more specifically, a rotated Reuleaux Pentagon. Due to the limitation of my mathematical understanding, I can only plot them using three functions and use RevolutionPlot3D to create graph. However, I don't really know how to combine them. The following code for two of the three parts don't seem to work:
Show[RevolutionPlot3D[{Sqrt[
1 - (t - Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]))^2] - 1/2}, {t,
Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]), Sin[(72 \[Pi])/180]},
RevolutionAxis -> "X"],
RevolutionPlot3D[{Sqrt[1 - t^2]}, {t, Sin[(72 \[Pi])/180], 1},
RevolutionAxis -> "X"]]
If you try and plot them one by one, it is quite easy to see how the graph created with the "Show" function doesn't work. Graphs one by one:
RevolutionPlot3D[{Sqrt[
1 - (t - Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]))^2] - 1/2}, {t,
Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]), Sin[(72 \[Pi])/180]},
RevolutionAxis -> "X"]
RevolutionPlot3D[{Sqrt[1 - t^2]}, {t, Sin[(72 \[Pi])/180], 1},
RevolutionAxis -> "X"]
If done properly, I think they should line up seamlessly. Does any one have any idea about it?