Dimensions of Space
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Point, Line, Plane Cube, Tesseract...
The animation at left, depicts the growing of a Crystal Octachoron, through the 4 Spatial Dimensions. This series of Point, Line, Plane… has proven to be a beneficial learning model for understanding Dimensionality.
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.
Continuous Trans-Dimensionalization
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.
Truncated Cubicons
Much like their 3D Platonic counterparts, the Higher Dimensional Forms can be modified (though sometimes with unexpected results). At left is a Tesseract with its corners ‘shaved off’.
Here is the ‘wire-frame’ version of it so you can see the unexpected Interior Complexity of its multi-chambered constitution.
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Interior Aspects of a Klein Bottle
Above, we see that the Klein Bottle is topologically composed of two Chirally Complemented Möbius strips.
