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 , Half Square Kite , Right Kite , Kite , Right Trapezoid , Isosceles Trapezoid , Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Antiparallelogram , House-Shape , Symmetric Pentagon , Concave Pentagon , Parallelogon , Stretched Hexagon , Arrow-Hexagon , L-Shape , Sharp Kink , Truncated Square , Frame , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Cross , Oktagram , Star of Lakshmi , Polygram , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Round Corner , Circular Corner , Circle Tangent Arrow , Crescent , Pointed Oval , Lancet Arch , Knoll , Annulus , Annulus Sector , Curved Rectangle , Rounded Polygon , Rounded Rectangle , Ellipse , Semi-Ellipse , Elliptical Segment , Elliptical Sector , Elliptical Ring , Stadium , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Tricorn , Interarc Triangle , Circular Arc Triangle , Arbelos , Salinon , Lune , Three Circles , Polycircle , Round-Edged Polygon , Rose , Gear , Oval , Egg-Profile , Lemniscate , Squircle , Digon , Spherical Triangle
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 , Rhombicosidodecahedron , Truncated Icosidodecahedron , Snub Dodecahedron
Catalan Solids: Triakis Tetrahedron , Rhombic Dodecahedron , Triakis Octahedron , Tetrakis Hexahedron , Deltoidal Icositetrahedron , Hexakis Octahedron , Rhombic Triacontahedron , Triakis Icosahedron , Pentakis Dodecahedron , Pentagonal Icositetrahedron , Deltoidal Hexecontahedron , Hexakis Icosahedron , Pentagonal Hexecontahedron
Johnson Solids: Pyramids , Cupolae , Rotunda , Elongated Pyramids , Gyroelongated Pyramids , Bipyramids , Elongated Bipyramids , Disheptahedron , Snub Disphenoid , Sphenocorona , Disphenocingulum
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 , Wedge-Cuboid , Half Cuboid , Skewed Cuboid , Skewed Three-Edged Prism , Obtuse Edged Cuboid , Elongated Dodecahedron , Truncated Rhombohedron , Hollow Cuboid , Hollow Pyramid , Hollow Frustum , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron , Great Dodecahedron , Great Icosahedron
Round Forms: Sphere , Hemisphere , Spherical Corner , Cylinder , Cut Cylinder , Oblique Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Bicone , Truncated Bicone , Rounded Cone , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Wedge , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Conical Sector , Conical Wedge , Spherical Shell , Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Spindle Torus , Toroid , Torus Sector , Toroid Sector , Arch , Reuleaux-Tetrahedron , Capsule , Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids
4D
Tesseract , Hypersphere
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Icosahedron Calculator
Calculations in a regular icosahedron, a solid with twenty faces, edges of equal length and angles of equal size. Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
A = 5 * a² * √3
V = 5 / 12 * a³ * ( 3 + √5 )
d = 2 * r_{c}
r_{c} = a / 4 * √10 + 2 * √5
r_{m} = a / 4 * ( 1 + √5 )
r_{i} = a / 12 * √3 * ( 3 + √5 )
A/V = 12 * √3 / ( ( 3 + √5 ) * a )

The regular icosahedron is a Platonic solid. Edge length and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^{-1} .

Net of an icosahedron, the three-dimensional body is unfolded in two dimensions.

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