Cubes and dodecahedra in hyperbolic space @ZenoRogue

Uploaded January 2020 | Updated September 2026, 1 week ago

Dodacedra growing until they fill the whole hyperbolic space.

Every dodecahedron has an inscribed transparent cube. While these cubes do not fill the hyperbolic space (only 40%), the rest can be filled with the same cubes (each dodecahedron is split into one cube and six quartercubes).

This relationship of {5,3,4} and {4,3,5} honeycombs has been observed by MagmaMcFry in the HyperRogue discord server.

Cubes and dodecahedra in hyperbolic space

$Non-Euclidean auralization Vampires have no reflection, but what about reverberation? Is their voice reflected by walls? (Watch this with sound! Thanks to @canana_man on Twitter for the inspiration.) 0:00 {3,4,4} hyperbolic honeycomb Vertices are ideal (infinitely far away) so we were moving at very large speeds. Some of the weirdness in the previous animation was just the plain old Doppler effect. 0:20 {5,3,4} hyperbolic honeycomb 0:40 {4,3,4}, Euclidean cubic honeycomb 1:00 {3,3,4}, aka 16-cell. Spherical geometry is weird as usual can you hear how long does it take the sound to travel around the sphere? The bird is the sound source, it raises its wings while it emits sound. 1:20 Here the sound speed is set very low. The Doppler effect is even more psychodelic if it increases the pitch of the original while decreasing the pitch of some reflections. 2:00 Sharper sound Like the first part but we used a sharper sound.$