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Geometry | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner, Formen

  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, Circular Corner, Pointed Oval, 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, Rhombicosidodecahedron, Truncated Icosidodecahedron

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

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, Wedge-Cuboid, 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, Spindle Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids
4D Tesseract, Hypersphere


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Great Stellated Dodecahedron Calculator

Calculations in a great stellated dodecahedron. This is the second of four Kepler-Poinsot polyhedra or regular star polyhedra, which are regular, non-convex (concave) polyhedra. The great stellated dodecahedron is made from an icosahedron with edge length a, whose edges are extended so that three meet in one point. As a result, a fitting right pyramid with an equilateral triangle as base is attached to each of its faces. The sides of the pyramid are isosceles triangles, the ratio of ridge s to edge a is that of the golden ratio, like in the pentagram b to c. s, c and A are the same as at the small stellated dodecahedron. Enter one value and choose the number of decimal places. Then click Calculate.


Johannes Kepler Edge length (a): Great Stellated Dodecahedron
12 faces, 60 sides, 30 edges a, 60 ridges s, 20 peaks
Faces: 12 pentagrams with chord length c, 3 meeting at each vertex
Sides: isosceles triangles with legs s and base a
Ridge length (s):
Pentagram chord (c):
Circumsphere radius (rc):
Pyramid height (hp):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.



Formulas:
s = a/2 * ( 1 + √5 ) = a * φ
c = a * ( 2 + √5 ) = a + 2s
rU = a/4 * √3 * ( 3 + √5 )
hp = a/6 * √3 * ( 3 + √5 )
A = 15a² * √5 + 2√5
V = 5/4a³ * ( 3 + √5 )

Golden ratio phi:
φ = ( 1 + √5 ) / 2 = 1.618033988749895...

Length, radius and height have the same unit (e.g. meter), surface areas have 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.




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