Triangular bipyramid (no ontology)

From Hi.gher. Space

The triangular bipyramid is the tegum product of a triangle with a digon. If the faces are equilateral triangles, it is one of the 92 Johnson solids, J₁₂. This form can be produced by joing two tetrahedra at the base.

Coordinates

The coordinates of a triangular bipyramid with side 2 are:

(±1, -√3/3, 0)
(0, 2√3/3, 0)
(0, 0, ±2√6/3)

Equations

• Variables:

l ⇒ length of edges of triangular bipyramid

• The hypervolumes of a triangular prism are given by:

total edge length = 9l
surface area = ^3√3∕₂ · l²
volume = ^√2∕₆ · l³

• The planar cross-sections (n) of a triangular prism are:

[!x,!y] ⇒ Unknown [!z] ⇒ triangle

Incidence matrix