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Home | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner

2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, Hexadecagon, 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, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Ellipse, Elliptical Segment, Stadium, Digon, Spherical Triangle, Spiral, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, 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, Skewed 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, Flat End Cylinder, Spherical Shell, Cylindrical Shell, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


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Trapezohedron Calculator

Calculations in regular tetragonal (4-) and pentagonal (5-) trapezohedrons. The number n of the trapezohedron refers to the number of faces of one half. A trapezohedron (or deltohedron) is a bipyramid, that is twisted in itself for 180°/n. A regular trapezohedron is the dual body of a unifrom antiprism. The faces are 2n deltoids. Choose the type of trapezohedron (4- or 5-), enter one value and choose the number of decimal places. Then click Calculate.



Euclid Trapezohedron: Tetragonal Trapezohedron
Tetragonal trapezohedron
8 faces, 16 edges, 10 vertices
Pentagonal Trapezohedron
Pentagonal trapezohedron
10 faces, 20 edges, 12 vertices
Edge length antiprism (z):
Short edge (a):
Long edge (b):
Height (h):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.




Formulas:

Tetragonal trapezohedron:
a = √ √2 - 1 * z
b = √ 2 * ( 1 + √2 ) / 2 * z
h = √ 1/2 * (4 + 3 * √2 ) * z
A = 2 * √ 2 + 4 * √2 * z²
V = 1/3 * √ 4 + 3 * √2 * z³

Pentagonal trapezohedron:
a = ( √5 - 1 ) / 2 * z
b = ( √5 + 1 ) / 2 * z
h = √ 5 + 2 * √5 * z
A = √ 25/2 * ( 5 + √5 ) * z²
V = 5/12 * ( 3 + √5 ) * z³


Edge lengths and height 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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