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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, 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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Johnson Pyramids Calculator

Calculations with Johnson pyramids. Johnson solids are convex polyhedra with regular polygon faces, that are not Platonic or Archimedean solids, prisms or antiprisms. Square (J1) and pentagonal (J2) pyramid are the first two of the 92 Johnson solids. Enter the type of pyramid and one value and choose the number of decimal places. Then click Calculate.



Euklid Type of pyramid: Square pyramid
Square pyramid, J1
5 faces, 8 egdes, 5 vertices
Base surface: square,
Side surfaces: 4 equilateral triangles

Pentagonal pyramid
Pentagonal pyramid, J2
6 faces, 10 egdes, 6 vertices
Base surface: regular pentagon,
Side surfaces: 5 equilateral triangles
Edge length (a):
Height (h):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.




Formulas:

Square pyramid:
h = a / √2
A = ( 1 + √3 ) * a²
V = √2 / 6 * a³

Pentagonal pyramid:
h = √ ( 5 - √5 ) / 10
A = [ √ ( 25 + 10√5 ) / 4 + 5√3 / 4 ] * a²
V = ( 5 + √5 ) / 24 * 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. See also square pyramid, regular pyramid.




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