# Question:Missing a certain polyhedron

## Question:Missing a certain polyhedron

Maple

Dear Maple users

I am delighted that Maple has builtin commands to plot so many polyhedrons in 3D. Here I am talking about the polyhedraplot command in the plots package. I was however disappointed that the socalled Truncated Icosahedron is not supported (not present in the supported list ...). My first question is:

1. Why isn't it supported?

It seems more relevant than many of the other polyhedrons which are supported. It is a member of the Archimedian Solids (see https://en.wikipedia.org/wiki/Truncated_icosahedron). Besides it is the basic structure for soccer footballs. I found out that a TruncatedIcosahedron command is available in the geom3d package. This command is able to deliver data for the faces and more. With this command I succeded in writing a small program to actually plot this polyhedron in 3D:

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restart;
with(geom3d):
with(plots):
TruncatedIcosahedron(football,point(C,(0,0,0)),1):

PlotFootball:=proc(tr::float)

local i::integer,
FootballFace::Vector(datatype=float[8]),
plotFace::Vector(datatype=float[8]);

for i from 1 to 32 do
FootballFace[i]:=faces(football)[i];
plotFace[i]:=polygonplot3d(Matrix(FootballFace[i]),axes=none,scaling=constrained,transparency=tr);
end do;

display(seq(plotFace[i],i=1..32)):

end proc:

PlotFootball(0.00);

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Since I am not really experienced in programming in Maple, here is my last question:

2. Can I simplify something in my code above?

Best wishes,

Erik

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