Geometry | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner, Formen

 
1DLine, Circular Arc, Parabola, Helix, Koch Curve
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, 1/2 EL Triangle, Golden Triangle, Quadrilateral, Rectangle, Golden Rectangle, Rhombus, Equidiagonal Rhombus, Parallelogram, Kite, 60-90-120 Kite, Half Square Kite, Right Kite, Trapezoid, Right Trapezoid, Isosceles Trapezoid, Tri-equilateral Trapezoid, Obtuse Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Crossed Rectangle, Antiparallelogram, House-Shape, Symmetric Pentagon, Diagonally Bisected Octagon, Cut Rectangle, Triangle Segment, Concave Pentagon, Concave Regular Pentagon, Stretched Pentagon, Straight Bisected Octagon, Stretched Hexagon, Symmetric Hexagon, Semi-regular Hexagon, Parallelogon, Concave Hexagon, Arrow-Hexagon, Rectangular Hexagon, L-Shape, Sharp Kink, T-Shape, Square Heptagon, Truncated Square, Stretched Octagon, Frame, Open Frame, Grid, Cross, X-Shape, H-Shape, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Double Star Polygon, Polygram, Concave Polygon, The Hat, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Circular Central Segment, Round Corner, Circular Corner, Circle Tangent Arrow, Drop Shape, Crescent, Pointed Oval, Two Circles, Lancet Arch, Knoll, Elongated Semicircle, Annulus, Semi-Annulus, Annulus Sector, Annulus Segment, Annulus stripe, Curved Rectangle, Cash, Rounded Polygon, Rounded Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Kepler Sector, Elliptical Ring, Elliptical Crescent, Stadium, Half Stadium, Stadium Segment, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Double Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Catenary Arc, Heart, Tricorn, Pointed Semicircle, Interarc Triangle, Circular Arc Triangle, Interarc Quadrangle, Intercircle Quadrangle, Circular Arc Quadrangle, Circular Arc Polygon, Claw, Half Yin-Yang, Arbelos, Salinon, Bulge, Lune, Three Circles, Polycircle, Round-Edged Polygon, Rose, Gear, Oval, Egg-Profile, Lemniscate, Squircle, Circular Square, 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, Gyroelongated Pyramids, Bipyramids, Elongated Bipyramids, Gyroelongated Square Dipyramid, Gyrobifastigium, Disheptahedron, Snub Disphenoid, Sphenocorona, Disphenocingulum

Other Polyhedrons:
Cuboid, Square Pillar, Triangular Pyramid, Square Pyramid, Regular Pyramid, Rectangular Pyramid, Pyramid, Square Frustum, Regular Frustum, Rectangular Frustum, Frustum, Bent Pyramid, Regular Bipyramid, Bipyramid, Bifrustum, Frustum-Pyramid, Ramp, Right Wedge, Wedge, Half Tetrahedron, Rhombohedron, Parallelepiped, Regular Prism, Prism, Oblique Prism, Anticube, Antiprism, Isosceles Antiprism, Prismatoid, Trapezohedron, Deltohedron, Disphenoid, Corner, General Tetrahedron, Wedge-Cuboid, Half Cuboid, Skewed Cuboid, Ingot, Skewed Three-Edged Prism, Cut Cuboid, Truncated Cuboid, Obtuse Edged Cuboid, Elongated Dodecahedron, Truncated Rhombohedron, Obelisk, Bent Cuboid, Hollow Cuboid, Hollow Pyramid, Hollow Frustum, Star Pyramid, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Great Dodecahedron, Great Icosahedron

Round Forms:
Sphere, Hemisphere, Quarter Sphere, Spherical Corner, Cylinder, Cut Cylinder, Oblique Cylinder, Bent Cylinder, Elliptic Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Truncated Elliptic Cone, General Cone, General Truncated Cone, Bicone, Truncated Bicone, Pointed Pillar, Rounded Cone, Elongated Hemisphere, Drop, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Central Segment, Spherical Wedge, Double Calotte, Rounded Disc, Double Sphere, Sphere Cone, Half Cylinder, Diagonally Halved Cylinder, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Half Cone, Conical Sector, Conical Wedge, Spherical Shell, Half Spherical Shell, Spherical Shell Cap, Cylindrical Shell, Cut Cylindrical Shell, Oblique Cylindrical Shell, Hollow Cone, Truncated Hollow Cone, Spherical Ring, Torus, Spindle Torus, Toroid, Torus Sector, Toroid Sector, Arch, Reuleaux-Tetrahedron, Capsule, Half Capsule, Capsule Segment, Double Point, Anticone, Truncated Anticone, Sphere-Cylinder, Lens, Concave Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Catenoid, Catenary Dome, Oloid, Steinmetz Solids, Cross Cylinder, Solid of Revolution
4D Tesseract, Hypersphere

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Johnson Bipyramids Calculator

Calculations with Johnson bipyramids or regular bipyramids. The triangular bipyramid (J12) is a double tetrahedron. The pentagonal bipyramid (J13) is made of two pentagonal Johnson pyramids which are stuck together at their bases. A square bipyramid would be an octahedron.
Enter the type of bipyramid and one value and choose the number of decimal places. Then click Calculate.


Norman Johnson Type of bipyramid: Triangular bipyramid
Triangular bipyramid, J12
6 faces, 9 egdes, 5 vertices
Side surfaces: equilateral triangles

Pentagonal bipyramid
Pentagonal bipyramid, J13
10 faces, 15 egdes, 7 vertices
Side surfaces: equilateral triangles
Edge length (a):
Height (h):
Surface area (A):
Volume (V):
Surface-to-volume ratio (A/V):
Round to    decimal places.




Formulas:

Triangular bipyramid:
h = 2/3 * √6 * a
A = 3/2 * √3 * a²
V = √2 / 6 * a³

Pentagonal bipyramid:
h = 2 * √ ( 5 - √5 ) / 10 * a
A = 5√3 / 2 * a²
V = ( 5 + √5 ) / 12 * 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.

The two Johnson bipyramids are two of the five Johnson solids whose faces consist solely of equilateral triangles. The other three are the gyroelongated square bipyramid (J17), the triaugmented triangular prism (J51), and the snub disphenoid (J84).
Both Johnson bipyramids have a plane of symmetry along the base of their single pyramids. In addition, they have a further number of planes of symmetry corresponding to the number of vertices at the base. These planes pass through both apexes of the bipyramid, through one vertex of the base, and through the midpoint of the opposite edge. Thus, the triangular bipyramid has four planes of symmetry, and the pentagonal bipyramid has six. Both are also rotationally symmetric about an axis through both apexes: the triangular bipyramid at an angle of 120 degrees and multiples thereof, and the pentagonal bipyramid at an angle of 72 degrees and multiples thereof. There are additional horizontal axes of rotation, corresponding to the number of vertices at a base. These pass through of a side vertex and the opposite edge. The rotation angle for these axes is 180 degrees and multiples thereof.
Both Johnson bipyramids are not point-symmetric.



Last updated on 11/21/2025.

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