Kaleidocycle

{|class="wikitable" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="280" !bgcolor=#e7dcc3 colspan=2|Regular-based right pyramids |- |align=center colspan=2|240pxSix tetrahedra whose vertices meet at the center. Blue edges are doubled with pairs of faces hidden. |- |bgcolor=#e7dcc3|Faces||24 isosceles triangles |- |bgcolor=#e7dcc3|Edges||36 (6 as degenerate pairs) |- |bgcolor=#e7dcc3|Vertices||12 |- |bgcolor=#e7dcc3|Symmetry group||C3v, [3], (*33), order 6 |- |bgcolor=#e7dcc3|Properties||torus |- align=center |colspan=2|240pxNet |} 120px|thumb|A kaleidocycle before it is wrapped into a ring makes a chain of 6 disphenoids connected edge to edge. A kaleidocycle or flextangle is a flexible polyhedron connecting six tetrahedra (or disphenoids) on opposite edges into a cycle. If the faces of the disphenoids are equilateral triangles, it can be constructed from a stretched triangular tiling net with four triangles in one direction and an even number in the other direction.

The kaleidocycle has degenerate pairs of coinciding edges in transition, which function as hinges. The kaleidocycle has an additional property that it can be continuously twisted around a ring axis, showing 4 sets of 6 triangular faces. The kaleidocycle is invariant under twists about its ring axis by k\pi/2, where k is an integer, and can therefore be continuously twisted.