Six papers in geometry and number theory, written between 2023
and 2026. Each is deposited with a permanent DOI and published under CC BY 4.0.
Several of them meet at the same number: the cube has 26 characteristic
elements, 26 is the only integer wedged between two perfect powers, and 26 is
the magic sum of the sieve model.
The magic hexagram mounted on Escher's solid, the stellated rhombic dodecahedron. Three sieves — equilibrium, unambiguity, reliability — reduce a factorial numbering larger than the atom count of the Solar System to a bounded landscape whose full census is 6,223,974 pyramid-magic numberings, with one singularity. Put forward as a candidate vocabulary for the diagnosis of rare disease.
Three studies of a memory, strategy and lottery game. How many categories the Feast admits; whether two perfect readers of one shuffle differ, one following the loops and one scanning the rows; and where the depth of the game comes from. Built on permutation cycles and the author's own integer sequence.
The cube has 26 characteristic elements and the English alphabet has 26 letters. Labelling one with the other gives the English Cube, whose 253 connecting segments have a constant total length — 280.9107 for the unit cube. With the notation, the eight segment classes, and the (MN) sign designed for it.
A tetradecahedron from the truncated cube, and the Eternal Flame of the Dohány Street Synagogue
A cube truncated into a solid of 14 faces — 2 squares, 4 hexagons, 8 triangles — then augmented with twelve pyramids: the lantern of the Eternal Flame above the bimah of the Great Synagogue in Budapest. Three specialists in polyhedral geometry each drew it, and none had seen it before.
Bilingual, English and Hungarian · with two animations
26 is the only integer directly sandwiched between perfect powers. A fresh approach to that folklore problem, congruent to the case of integer 2 in Pillai's conjecture, introducing coefficial divisibility, the multimorphic integer and the transdimensional number.
Cube edge times body- over face-diagonal equals the diameter of the largest inscribed circle
The largest circle a cube will hold is wider than the cube's own edge. Stated as a sentence, needing no square roots: they appear only in the proof. Two extensions follow, to the cube's largest inscribed triangle and square.