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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, 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, 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, Crescent, 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, 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, Disheptahedron, Snub Disphenoid, Sphenocorona

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


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Unicursal Hexagram Calculator

Calculations in a unicursal hexagram. This is made of two long and four short diagonals of a hexagon. Other than a regular hexagram, this can be drawn in one go, without lifting the pen. The short diagonal b is split into three pieces of different length, the long diagonal c is split into four pieces of equal length. Both large spikes have an angle of 60°, the four small spikes are rectangular to the large ones. The area is calculated as that of a rhombus with the side length b1+b2 plus the equal right triangles of the four small spikes. Enter one value and choose the number of decimal places. Then click Calculate.


Blaise Pascal Edge length hexagon (a): Unicursal Hexagram
Unicursal Hexagram with caption
Short diagonal (b):
Long diagonal (c):
Section b1:
Section b2:
Section b3:
Sections c':
Perimeter (p):
Area (A):
Round to    decimal places.



Formulas:
b = √3 * a
b1 = b/2 = √3 / 2 * a
b2 = b/6 = √3 / 6 * a
b3 = b/3 = √3 / 3 * a
c = 2 * a
c' = c/4 = a/2
p = 4b1 + 4b3 + 4c' = ( 2 + 10/3 * √3 ) * a
A = ( b1 + b2 )² * sin(60°) + 2b2c' = 5/6 * √3 * a²

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




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