progressive 3D slices of a hypercube

3D slices of a 24-cell

These are 3D slices of a 4D hypershape known as the dodecacontachoron (120-cell) which is a tessellation of the hypersphere by 120 dodecahedrons.

Progressive 3D slices of the 4-dimensional hypertorus. Notice the discrete critical points as the slice changes topology from a sphere, to a torus, then a genus-2 surface, with the equatorial slice being two separate tori.

Slicing the 4D hypertorus again. This time the slice hyperplane is tilted and the locations of the 8 critical points are shifted, altering their sequencing. As a result, the equatorial slice is not a pair of disjoint tori, but instead is a surface of genus 3.

Hypertorus rotating through a fixed set of slice planes spaced evenly along the w-axis

A sequence of (generalized) Penrose tilings

4D Hypertorus passing through 3D Flatland

Penrose tilings made using de Bruijn's multigrid method. These have a nice effect when zoomed out. Made using @Wolfram language. Notebook available here: community.wolfram.com/groups/-/m/t/2…

Aperiodic 7-fold rhombic tilings

Hypertorus with three half-twists. Some of the equatorial slices are trefoil knots.

Rhombic tiling using de Bruijn's multi-grid method. This tiling uses a 49-grid pattern. Perturbations in the tiling are contrained so as to preserve 7-fold rotational periodicity.

a sequence of rhombic tilings with 3-fold rotational symmetry

another look at adding twists to the hypertorus here, two different twisting axes are compared

3D equatorial slice of a rotating 120-cell (4D polytope with dodecahedral facets)

Alex Kontorovich will be in Austin next week. Would be awesome if we had an opportunity to engage with him. x.com/AlexKontorovic…

Excited to accompany Stephen Wolfram at the augmentation lab Human Augmentation Summit hosted by the MIT Media Lab MIT Media Lab. Looking forward to present my work and to see what awesome projects have been created! ekkolapto Curt Jaimungal Daniel Van Zant