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2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, N-gon

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Rhombus, Parallelogram, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Threestar, Fourstar, Pentagram, Hexagram, Oktagram, Star of Lakshmi

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Ellipse, Elliptical Segment, Stadium, Digon, Spherical Triangle, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Parabolic Segment, Arbelos, Salinon, Lune, Oval, Three Circles, Lemniscate, Squircle
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:
Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Rhombic Triacontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Snub Disphenoid

Other Polyhedrons:
Cuboid, Square Pillar, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Bipyramid, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Half Cuboid, Truncated Rhombohedron, 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, Spheroid, Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Spherical Shell, Cylindrical Shell, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


General Tetrahedron Calculator

Calculations in 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.

Leonhard Euler, by Jakob Emanuel Handmann Side a: General Tetrahedron
4 faces, 6 edges, 4 vertices
Faces: triangles
Side b:
Side c:
Side a':
Side b':
Side c':
Intermediate value fa:
Intermediate value fb:
Intermediate value fc:
Intermediate value δ:
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.


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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