Mathematical Experiment 5

No class on March 26

Construct the part of the cylinder

x2 + y2 =  1

lying between the planes z= -1 and z = x.

Combine the above surface with its reflection across the plane x = z to form this model.

Join four cylinders of the same size symmetrically as thus:

Join eight cylinders of the same size symmetrically as thus:

Join six cylinders of the same size symmetrically as thus:

Construct three mutually orthogonal "golden rectangles" whose 12 vertices form a regular icosahedron. Let n denote the golden ratio

n = .

the vertices may be placed on

 [+n, +1, 0],  [0, +n, +1],  [+1,0, +n].

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Join 12 cylinders of the same size symmetrically as thus:

Let n denote the golden ratio

n = .

Illustrate this interesting fact: the points

 [+n, +n-1, 0], [0, +n, +n-1],

[+n-1, 0, +n], [+1, +1, +1]

comprise the vertices of a regular dodecahedron.

Construct the small stellated dodecahedron using the library geom3d:

Construct the small stellated dodecahedron using the library plottools: