Atlas of neoplatonic solids

A neoplatonic solid is an undented Euclidean polyhedron with equilateral triangle faces, meeting at most six to a vertex. More →

The paper: Peter Doyle and Matthew Ellison, Neoplatonic solids, arXiv:2607.26363.

Archives & code: atlas doi:10.5281/zenodo.21367249 · prime census doi:10.5281/zenodo.19761389 · proof software doi:10.5281/zenodo.21609862 · source github.com/peterdoyle1717/neoplatonic-atlas

Themed galleries

Primes v≤12 Primes v=13 Primes v=14 Non-prime Platonic & Archimedean Convex Hyperbolic Dented Hull-buried Pancakes Floppy Symmetry Eisenstein subdivisions All angles recognized Cap-replaced convex (3,1) (2,2) (4,1) (5,1) Preapproved Tough cases

Example

Each neoplatonic has its own page — the Euclidean solid, the ideal net, the CLERS triangulation, and, where the development from the ideal limit is certified, the morph in the Poincaré and Klein models. Click the CLERS code under the model to the right to open its page.
v9CCCACACACACAAE

Quick links by size

v=4 v=5 v=6 v=7 v=8 v=9 v=10 v=11 v=12 v=13 v=14
v=15 v=16 v=17 v=18 v=19 v=20 v=21 v=22 v=23 v=24 v=25 v=26 v=27 v=28 v=29 v=30 v=32 v=34 v=35 v=37 v=38 v=40 v=42 v=44 v=47 v=48 v=49 v=50 v=51 v=52 v=54 v=56 v=57 v=58 v=62 v=63 v=64 v=65 v=66 v=67 v=72 v=74 v=76 v=78 v=80 v=82 v=83 v=86 v=88 v=90 v=92 v=93 v=97 v=98 v=99 v=100 v=102 v=106 v=107 v=110 v=114 v=116 v=122 v=127 v=128 v=130 v=132 v=135 v=137 v=146 v=149 v=152 v=162 v=164 v=177 v=182 v=191 v=192 v=200 v=202 v=212 v=218 v=226 v=227 v=236 v=244 v=252 v=272 v=290 v=296 v=326 v=340 v=352 v=354 v=386 v=394 v=418 v=443 v=452 v=506 v=552 v=650 v=794

Find a net

CLERS code, e.g. CCCACACACACAAE

CC0: to the extent possible under law, Peter Doyle has waived all copyright and related and neighboring rights to this atlas.