1D Line
2D
Regular Polygons: Equilateral Triangle , Square , Pentagon , Hexagon , Heptagon , Octagon , Nonagon , Decagon , Hendecagon , Dodecagon , Hexadecagon , N-gon , Polygon Ring
Other Polygons: Triangle , Right Triangle , Isosceles Triangle , IR Triangle , Quadrilateral , Rectangle , Rhombus , Parallelogram , Right Kite , Kite , Right Trapezoid , Isosceles Trapezoid , Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Antiparallelogram , House-Shape , Symmetric Pentagon , Concave Pentagon , Parallelogon , Arrow-Hexagon , Sharp Kink , Frame , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Cross , Oktagram , Star of Lakshmi , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Round Corner , Annulus , Annulus Sector , Curved Rectangle , Ellipse , Semi-Ellipse , Elliptical Segment , Elliptical Sector , Stadium , Digon , Spherical Triangle , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Arbelos , Salinon , Lune , Three Circles , Polycircle , Oval , Lemniscate , Squircle
3D
Platonic Solids: Tetrahedron , Cube , Octahedron , Dodecahedron , Icosahedron
Archimedean Solids: Truncated Tetrahedron , Cuboctahedron , Truncated Cube , Truncated Octahedron , Rhombicuboctahedron , Truncated Cuboctahedron , Icosidodecahedron , Truncated Dodecahedron , Truncated Icosahedron , Snub Cube
Catalan Solids: Triakis Tetrahedron , Rhombic Dodecahedron , Triakis Octahedron , Tetrakis Hexahedron , Deltoidal Icositetrahedron , Hexakis Octahedron , Rhombic Triacontahedron , Pentakis Dodecahedron , Pentagonal Icositetrahedron
Johnson Solids: Pyramids , Cupolae , Rotunda , Elongated Pyramids , Snub Disphenoid
Other Polyhedrons: Cuboid , Square Pillar , Triangular Pyramid , Square Pyramid , Regular Pyramid , Pyramid , Regular Frustum , Frustum , Bipyramid , Bifrustum , Ramp , Right Wedge , Wedge , Rhombohedron , Parallelepiped , Prism , Oblique Prism , Antiprism , Prismatoid , Trapezohedron , Disphenoid , Corner , General Tetrahedron , Half Cuboid , Skewed Cuboid , Skewed Three-Edged Prism , Truncated Rhombohedron , Hollow Cuboid , Hollow Pyramid , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron
Round Forms: Sphere , Hemisphere , Cylinder , Cut Cylinder , Oblique Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Bicone , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Wedge , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Spherical Shell , Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Arch , Reuleaux-Tetrahedron , Capsule , Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids
4D
Tesseract , Hypersphere
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Hypocycloid Calculator
Calculations with hypocycloids. A hypocycloid is the curve that is generated by a point of a small circle , which is rolling inside a large circle. The ratio of the radiuses of the two circles must be an integer. This ratio determines the number of cusps. The astroid is a hypocycloid with four cusps. Enter at radiuses and number of cusps two values and choose the number of decimal places. Then click Calculate. n must be an integer >2.

Generation of a hypocycloid.

Formulas:
n = a / b
l = 2 * a * sin (π/n)
p = 8 * a * ( n - 1 ) / n
A = π * a² * ( n - 1 ) * ( n - 2 ) / n²
pi:
π = 3.141592653589793...

Radius, length and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

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