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For x(0)=a, x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)]. (2) If a/b=n, then x = 1/(n-2)[(n-1)cosphi-cos[(n-1)phi]a (3) y = ...

The hypocycloid x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)] (2) has involute x = (a-2b)/a[(a-b)cosphi+bcos((a-b)/bphi)] (3) y = ...

The pedal curve for an n-cusped hypocycloid x = a((n-1)cost+cos[(n-1)t])/n (1) y = a((n-1)sint-sin[(n-1)t])/n (2) with pedal point at the origin is the curve x_p = ...

The evolute of a hypotrochoid is a complicated equation. Examples are illustrated above.

A 20-sided polygon. The regular icosagon is a constructible polygon, and the regular icosagon of unit side length has inradius r, circumradius R, and area A given by r = ...

A number of attractive 10-compounds of the regular icosahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 11-compounds of the regular icosahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 2-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 5-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 6-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...