2 problems

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Conjecture on multiple $k$ -isohedral tilings by Type 7–13 convex pentagonal monotiles
Multiple-tiling conjecture. Convex pentagonal monotiles belonging to the Type 7–13 families, but not contained in $T_1$ or $T_2$ , are unlikely to generate multiple types of $k$ -iso…
Conjectureopenconvex-polygons isohedral-tilings tilingsarXiv posted 2 days ago
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The convex-tile inverse Grünbaum–Shephard conjecture for spherical monohedral tilings
Convex-tile inverse Grünbaum–Shephard conjecture. For every normal spherical monohedral tiling topologically a Platonic solid, an Archimedean dual, an $n$ -gonal bipyramid, or an…
Conjectureopenconvex-geometry isohedral-tilings spherical-tilingsarXiv posted 2 days ago

Conjecture on multiple kkk-isohedral tilings by Type 7–13 convex pentagonal monotiles