Zalgaller's proof of 92 Johnson solids

Discussion of known convex regular-faced polytopes, including the Johnson solids in 3D, and higher dimensions; and the discovery of new ones.

Zalgaller's proof of 92 Johnson solids

Postby mr_e_man » Thu Apr 08, 2021 1:35 am

Quickfur, you can read Russian. What are the main ideas in Zalgaller's paper?

I think I can understand most of the paper, concerning trivalent and tetravalent vertices; I have been making similar pictures and calculations.

How does he handle pentavalent vertices, which have many degrees of freedom? I see some topological arguments involving the total numbers of elements of various types, and the graph formed by only-triangle vertices.

What is he doing in Figure 297? It reminds me of hyperbolic geometry, with equidistant curves and limiting-parallel lines.

Does he use the help of a computer? It looks like the work is mostly manual.
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
mr_e_man
Trionian
 
Posts: 187
Joined: Tue Sep 18, 2018 4:10 am

Return to CRF Polytopes

Who is online

Users browsing this forum: No registered users and 1 guest

cron