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.
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.
Cite this page: Rechneronline (2026) - Johnson Bipyramids: Triangular and Pentagonal Bipyramid. Retrieved on 2026-06-13 from https://rechneronline.de/pi/johnson-bipyramid.php