Dimensions of Space
Octachoron Crystal Net
The animation at the right depicts the unfurling of all 8 Cubic Crystals, through Space-Time until they reach the 3D Plane of the 8 Stacked Cubes. Then it will Engulf itself Retro-Causally to become the Tesseract once more. Watch as these astonishing Transitions morph Trans-Dimensionally!
3rd Dimensional Infinity
As you watch the long end of the cube-net (above) unfold and envelop the remaining cubes, it will be helpful to remember that this is only a drawing. In the ‘real’ 3D world, this enveloping process involves that it must jump out of the 3rd and into the 4th Dimension. That means that it will temporarily exceed the 3rd Dimensional Infinity and disappear! We know this from stereographic projections on a 4D hypercube. Where it goes when it disappears must rely on Projective Geometry to explain.
Perhaps most impressive of all is this Continuous Fourth Dimensional Morphing Sequence, made possible by the ability of a Higher Dimension to supersede the Dimensionality of its lower Dimensions! Represented here is animated Trans-Dimensional Emergence. Watch closely as the interior 3D cube unfolds to envelop the rest of the figure from the 4th Dimension.
Interior Aspects of a Klein Bottle
Above, we see that the Klein Bottle is topologically composed of two Chirally Complemented Möbius strips.