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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, Stretched Hexagon, Arrow-Hexagon, L-Shape, Sharp Kink, Truncated Square, Frame, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Cross, Oktagram, Star of Lakshmi, Polygram, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Circular Corner, 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, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Tricorn, Arbelos, Salinon, Lune, Three Circles, Polycircle, Round-Edged Polygon, Rose, Gear, Oval, Egg-Profile, Lemniscate, Squircle, 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, Elongated Bipyramids, Disheptahedron, Snub Disphenoid, Sphenocorona, Disphenocingulum

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, Obtuse Edged Cuboid, Elongated Dodecahedron, Truncated Rhombohedron, Hollow Cuboid, Hollow Pyramid, Hollow Frustum, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron

Round Forms:
Sphere, Hemisphere, Spherical Corner, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Bicone, Truncated Bicone, Rounded Cone, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Conical Sector, Conical Wedge, Spherical Shell, Cylindrical Shell, Hollow Cone, Truncated Hollow Cone, Spherical Ring, Torus, Spindle Torus, Toroid, Torus Sector, Toroid Sector, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids
4D Tesseract, Hypersphere


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Truncated Rhombohedron Calculator (Dürer's solid)

The truncated rhombohedron (also truncated triangular trapezohedron) is a polyhedron from Albrecht Dürer's engraving Melencolia I. It is constructed by truncating the two sharp vertices of a rhombohedron with the edge length a and an angular ratio of 2/3 (72° and 108°), so that the remaining solid has a circumscribed sphere, that touches every vertice.
Enter one value and choose the number of decimal places. Then click Calculate.


Albrecht Dürer Edge length rhombohedron (a): Dürer's truncated rhombohedron
8 faces, 18 edges, 12 vertices
Faces: 6 axial-symmetric pentagons, 2 equilateral triangles with side length c
Edge length (b):
Edge length triangle (c):
Circumsphere radius (rc):
Surface area (A):
Area of a pentagon (A5):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.



Formulas:
b = a/2 * ( 3 - √5 )
c = a * √5 - 2√5
rc = a/4 * √14 - 2√5
A = a²/2 * ( 3√5 + 2√5 + 5√3 - 2√15 )
A5 = a²/4 * √5 + 2√5
V = 5/3a³ * √√5 - 2
Source: de.wikipedia.org/wiki/Rhomboederstumpf, Frankee 67

Length and radius 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.



Albrecht Dürer Melencolia I
Albrecht Dürer, Melencolia I, engraving from 1514.


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