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The keratoid cusp is quintic algebraic curve defined by y^2=x^2y+x^5. (1) It has a ramphoid cusp at the origin, horizontal tangents at (0,0) and (-6/(25),(108)/(3125)), and a ...

The knot curve is a quartic curve with implicit Cartesian equation (x^2-1)^2=y^2(3+2y). (1) The x- and y-intercepts are (0,-1), (0,1/2), and (+/-1,0). It has horizontal ...

An equilateral parallelogram whose acute angles are 45 degrees. Sometimes, the restriction to 45 degrees is dropped, and it is required only that two opposite angles are ...

Am octagonal prims is a prism composed of octagonal faces. The regular right octagonal prism of unit edge length has surface area and volume S = 4(3+sqrt(2)) (1) V = ...

The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point ...

A 15-sided polygon, sometimes also called the pentakaidecagon. For a regular pentadecagon with side length 1, the inradius r, circumradius R, and area A are r = ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...

An epicycloid with n=5 cusps, named after the buttercup genus Ranunculus (Madachy 1979). Its parametric equations are x = a[6cost-cos(6t)] (1) y = a[6sint-sin(6t)]. (2) Its ...

The regular decagon is constructible 10-sided regular polygon with Schläfli symbol {10}. The inradius r, circumradius R, and area can be computed directly from the formulas ...

Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...