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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, 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, Star of Lakshmi

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Round Corner, Annulus, Annulus Sector, Ellipse, 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, 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, Reuleaux-Tetrahedron, Torus, Capsule, Lens, Barrel, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


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Cupola Calculator

Calculations in a regular cupola. A cupola is a polyhedron with two opposite polygons, of which one has twice as many vertices as the other and with alternating triangles and quadrangles as side faces. When all faces of the cupola are regular, then the cupola itself is regular and is a Johnson solid. There are three regular cupolae, the triangular (J3), the square (J4) and the pentagonal (J5) cupola. Enter the type of cupola and one value and choose the number of decimal places. Then click Calculate.



Euclid Type of cupola: Triangular cupola
Triangular cupola, J3
8 faces, 15 egdes, 9 vertices
Top surface: equilateral triangle,
Base surface: regular hexagon,
Side surfaces: 3 equilateral triangles, 3 squares

Square cupola
Square cupola, J4
10 faces, 20 egdes, 12 vertices
Top surface: square,
Base surface: regular octagon,
Side surfaces: 4 equilateral triangles, 4 squares

Pentagonal cupola
Pentagonal cupola, J5
12 faces, 25 egdes, 15 vertices
Top surface: regular pentagon,
Base surface: regular decagon,
Side surfaces: 5 equilateral triangles, 5 squares
Edge length (a):
Height (h):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.




Formulas:

h = a * √ 1 - 1/4 * csc² ( π / n )
n = number of vertices of the top surface

Triangular cupola:
A = ( 3 + 5 * √3 / 2 ) * a²
V = 5 / ( 3 * √2 ) * a³

Square cupola:
A = ( 7 + 2√2 + √3 ) * a²
V = ( 1 + 2√2 / 3 ) * a³

Pentagonal cupola:
A = 1/4 * [ 20 + 5√3 + √ 5 * ( 145 + 62√5 ) ] * a²
V = 1/6 * ( 5 + 4√5 ) * a³


Length 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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