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 , Golden Rectangle , Rhombus , Parallelogram , Half Square Kite , Right Kite , Kite , Right Trapezoid , Isosceles Trapezoid , Tri-equilateral Trapezoid , Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Crossed Rectangle , Antiparallelogram , House-Shape , Symmetric Pentagon , Cut Rectangle , Concave Pentagon , Concave Regular Pentagon , Parallelogon , Stretched Hexagon , Concave Hexagon , Arrow-Hexagon , Rectangular Hexagon , L-Shape , Sharp Kink , T-Shape , Truncated Square , Frame , Open Frame , Grid , Cross , X-Shape , H-Shape , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Oktagram , Star of Lakshmi , Double Star Polygon , Polygram , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Circular Central Segment , Round Corner , Circular Corner , Circle Tangent Arrow , Drop Shape , 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 , Double Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Heart , Tricorn , Interarc Triangle , Circular Arc Triangle , Interarc Quadrangle , Intercircle Quadrangle , Circular Arc Quadrangle , Circular Arc Polygon , Claw , Half Yin-Yang , Arbelos , Salinon , Bulge , Lune , Three Circles , Polycircle , Round-Edged Polygon , Rose , Gear , Oval , Egg-Profile , Lemniscate , Squircle , Circular Square , 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 , Gyroelongated Square Dipyramid , Gyrobifastigium , Disheptahedron , Snub Disphenoid , Sphenocorona , Disphenocingulum
Other Polyhedrons: Cuboid , Square Pillar , Triangular Pyramid , Square Pyramid , Regular Pyramid , Pyramid , Regular Frustum , Frustum , Regular Bipyramid , Bipyramid , Bifrustum , Frustum-Pyramid , Ramp , Right Wedge , Wedge , Half Tetrahedron , Rhombohedron , Parallelepiped , Regular Prism , Prism , Oblique Prism , Anticube , Antiprism , Prismatoid , Trapezohedron , Disphenoid , Corner , General Tetrahedron , Wedge-Cuboid , Half Cuboid , Skewed Cuboid , Ingot , Skewed Three-Edged Prism , Cut Cuboid , Truncated Cuboid , Obtuse Edged Cuboid , Elongated Dodecahedron , Truncated Rhombohedron , Obelisk , Bent Cuboid , Hollow Cuboid , Hollow Pyramid , Hollow Frustum , Star Pyramid , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron , Great Dodecahedron , Great Icosahedron
Round Forms: Sphere , Hemisphere , Spherical Corner , Cylinder , Cut Cylinder , Oblique Cylinder , Bent Cylinder , Elliptic Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Bicone , Truncated Bicone , Pointed Pillar , Rounded Cone , Drop , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Central Segment , Double Calotte , Spherical Wedge , Half Cylinder , Diagonally Halved Cylinder , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Half Cone , Conical Sector , Conical Wedge , Spherical Shell , Half Spherical Shell , Cylindrical Shell , Cut Cylindrical Shell , Oblique Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Spindle Torus , Toroid , Torus Sector , Toroid Sector , Arch , Reuleaux-Tetrahedron , Capsule , Capsule Segment , Double Point , Sphere-Cylinder , Lens , Concave Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids , Solid of Revolution
4D
Tesseract , Hypersphere
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General Tetrahedron Calculator
Calculations at a general tetrahedron. A tetrahedron is a polyhedron of four triangular faces. Mostly, the term tetrahedron is used for a regular tetrahedron , but here the general tetrahedron with different side lengths can be calculated. Its faces are the triangles (a, b, c), (a, b', c'), (a', b, c') and (a', b', c). The volume formula of the general tetrahedron was discovered by Leonhard Euler. Enter the six side lengths and choose the number of decimal places. Then click Calculate. In every triangle, any two sides together must be longer than the third side.

Formulas:
Perimeters of the triangles:
p = a + b + c
q = a + b' + c'
r = a' + b + c'
s = a' + b' + c
A = √p/2 * (p/2-a) * (p/2-b) * (p/2-c) + √q/2 * (q/2-a) * (q/2-b') * (q/2-c') + √r/2 * (r/2-a') * (r/2-b) * (r/2-c') + √s/2 * (s/2-a') * (s/2-b') * (s/2-c)
fa = b² + b'² + c² + c'² - a² - a'²
fb = a² + a'² + c² + c'² - b² - b'²
fc = a² + a'² + b² + b'² - c² - c'²
δ = a² * b² * c² + a² * b'² * c'² + a'² * b² * c'² + a'² * b'² * c²
V = √ a² * a'² * fa + b² * b'² * fb + c² * c'² * fc - δ / 12

The lengths 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} .

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