by **wendy** » Mon Oct 03, 2016 1:14 am

If you are familiar with complex numbers and analytic geometry, then using complex numbers in N-dimesional geometry, doubles the value of N of each space, so lines are 2d, hedrices are 4d, &c. Reflection (r -> -r) is replaced by r = r cis(wt) where cis = cos + i sin, and wt is omega (speed) * time, means in every even dimension things go around a centre.

The regular polytopes of p(4)2 have edges with p vertives, gives a 4d reflex of the p-gns in a bi-p-gonal prism, The dual is 2(4)p has edges that have 2 vertices, that run from diameter to diameter. 2(3)2(4)p has triangles wedged in the x,y,z axis. Likewise, the 5{3}5 has 120 edges, by considering the pentagons around the edges that the vertices fall in, when the figure is rotated 6/120 of a circle. This is the basis of the Poincare pentagonal tegum i showed John Conway.

The figure Richard gives of the thatched (tegum-sum) inverted tri-triangular prisms, is but the 2(4)3(3)3 with three orthogonal diameters removed. A similar effect is see in 3,3,5 = f3,4,3 + GAP.

The dream you dream alone is only a dream

the dream we dream together is reality.