Kaleidoscopic Cells

Many triply periodic minimal surfaces have embedded straight lines, which of necessity must be C2 symmetry axes (180 degree rotational symmetry). Possible C2 axes are shown in color below.

There are two classes of kaleidoscopic cells: the prisms and the tetrahedra. A prism in the general sense is a plane polygon extended at right angles in the third dimension. A tetrahedron is a polyhedron with four flat faces.

If you have Java enabled, the images should display as 3D objects movable with your mouse, courtesy of JavaView Lite. Right-clicking on an object will bring up a menu; in particular, "New display" will launch a dedicated window you can enlarge for better viewing.

Prisms

	Rectangular Parallelepiped A rectangular box, shown in its maximally symmetric form of a cube.
	Equilateral Prism A prism based on an equilateral triangle.
	Isosceles Prism A prism based on a 45-45-90 degree triangle.
	30-60-90 Prism A prism based on a 30-60-90 degree triangle.

Tetrahedra

	Quadrirectangular Tetrahedron This tetrahedron is shown as 1/48 of a cube; it is the fundamental region for the full symmetry group of the cube. There is one possible C2 axis, shown in green. The name quadrirectangular refers to the fact that each of the four faces has a right angle.
	Trirectangular Tetrahedron This tetrahedron is shown as 1/24 of a cube. There are no possible C2 axes.
	Tetragonal Disphenoid This tetrahedron can be viewed as two trirectangular tetrahedra stacked up. There are three possible C2 axes, shown in green and red.