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The n-cyclohedron, also known as the Bott-Taubes polytope, is defined as the compactification of the configuration space of n points on the circle. The cyclohedron can be ...

The evolute of the cycloid x(t) = a(t-sint) (1) y(t) = a(1-cost) (2) is given by x(t) = a(t+sint) (3) y(t) = a(cost-1). (4) As can be seen in the above figure, the evolute is ...

The involute of the cycloid x = a(t-sint) (1) y = a(1-cost) (2) is given by x_i = a(t+sint) (3) y_i = a(3+cost). (4) As can be seen in the above figure, the involute is ...

The radial curve of the cycloid with parametric equations x = a(t-sint) (1) y = a(1-cost) (2) is the circle x_r = x_0+2asint (3) y_r = -2a+y_0+2acost. (4)

A surface of revolution of the form r(phi)=a[1-esin^2phi-(3/8e^2+k)sin^2(2phi)], where k is a second-order correction to the figure of a rotating fluid.

A decagon is a ten-sided polygon. Several special types of decagons are illustrated above. In particular, a decagon with vertices equally spaced around a circle and with all ...

A decahedron is a polyhedron having 10 faces. Examples include the 5-trapezohedron, augmented pentagonal prism (Johnson solid J_(52)), augmented tridiminished icosahedron ...

For every partition of all the points on a line into two nonempty sets such that no point of either lies between two points of the other, there is a point of one set which ...

The evolute of a deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid evolute for n=3 x_e = 2cost-cos(2t) (3) y_e = 2sint+sin(2t), (4) which is ...

The involute of the deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid involute for n=3 x_i = 1/9[2cost-cos(2t)] (3) y_i = 1/9[2sint+sin(2t)], (4) ...