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  1D Line
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, Right Kite, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Sharp Kink, Frame, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Curved Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Stadium, Digon, Spherical Triangle, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Arbelos, Salinon, Lune, Three Circles, Oval, 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, Snub Cube

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, Bifrustum, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Prismatoid, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Half Cuboid, Skewed Cuboid, Skewed Three-Edged Prism, Truncated Rhombohedron, Hollow Cuboid, 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, Bicone, Spheroid, Ellipsoid, Semi-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


Elongated Pyramid Calculator

Calculations with regular elongated pyramids. These are three Johnson solids: the elongated triangular pyramid (J7) is a regular tetrahedron with a matching right prism attached to one face. Elongated square pyramid (J8) and elongated pentagonal pyramid (J9) are the two Johnson pyramids with matching cube, respectively prism attached. Enter the type of elongated pyramid and one value and choose the number of decimal places. Then click Calculate.

Euclid Type of elongated pyramid: Triangular pyramid
Elongated triangular pyramid, J7
7 faces, 12 egdes, 7 vertices
Pyramid faces: 3 equilateral triangles,
Side surfaces: 3 squares,
Base surface: equilateral triangle

Square pyramid
Elongated square pyramid, J8
9 faces, 16 egdes, 9 vertices
Pyramid faces: 4 equilateral triangles,
Side surfaces: 4 squares,
Base surface: squares

Pentagonal pyramid
Elongated pentagonal pyramid, J9
11 faces, 20 egdes, 11 vertices
Pyramid faces: 5 equilateral triangles,
Side surfaces: 5 squares,
Base surface: regular pentagon
Edge length (a):
Height (h):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.


Elongated triangular pyramid:
h = ( √6 / 3 + 1 ) * a
A = ( 3 + √3 ) * a²
V = ( √2 + 3√3 ) /12 * a³

Elongated square pyramid:
h = ( 1 / √2 + 1 ) * a
A = ( 5 + √3 ) * a²
V = ( 1 + √2 / 6 ) * a³

Elongated pentagonal pyramid:
h = ( √ ( 5 - √5 ) / 10 + 1 ) * a
A = [ √ ( 25 + 10√5 ) / 4 + 5√3 / 4 + 5 ] * a²
V = [ ( 5 + √5 ) / 24 + √ 25 + 10 * √5 / 4 ] * 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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