Multi Dimensional Geometry
The geometry of symmetrical shapes familiar from 3-D, viewed in their 4th or higher dimensional aspects.


Here is how we make a hypercube
then we can watch it's mysterious looking rotations
below: a square ascends the dimensional ladder - from left: 2-d square, 3-d cube, 4-d tesseract and 5-d hypercube

a view of the same process seen from another angle

In Geometry another dimension is simply another direction at right-angles to the previous -
since this creates a whole new type of space we can only view the "shadows" of 4-D objects in 3-Space. The shadow only r
epresents a vague outline of the true 4-D form. For example note that in Higher Dimensional space Rotation is percieved by us as
"turning inside out" as well as our normal concept of rotation Just as an object in 3-space creates a flat 2-D shadow that
changes shape when rotated, 4-dimensional objects can only be visualized as 'shadows' that are 3-D forms
which change when the objects is rotated in 4-Space.

Below is a rotating Four Dimensional Cube seen as it's shadow in 3-D space.
Notice how it fluidly turns inside out
from math.harvard.edu



Visionary Artist Paul Laffoley's Awesome Design of an Unfolded Hypercube House



Check out the Hyperspace Glossary!
http://members.aol.com/Polycell/glossary.html


This is the outline of some of the cubes within the hypercube (8 total)




Here is the process for constructing a hyper-pyramid