The properties of mosaic pentagons with a pair of equal adjacent edges
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1380-1412
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It was obtained by O.G. Bagina the complete classification of convex mosaic pentagons, admitting normal (edge to edge) tilings, in 2011–2012. The classification includes 8 types of such pentagons. In the proof of the completeness of this list the following fact was used. If a convex pentagon tiles the plane normally, belongs only the first type of the list and has only a pair of equal adjacent edges, that is, the angles and edges of this pentagon satisfy the relations $C_0 = C_1, x_2 + x_3 = 180^\circ$, then it angles satisfy also the relation $x_0 + 2x_1 = 360^\circ$. But this statement has not been proven. This paper fills this gap.
Keywords:
convex pentagon, mosaic pentagon, tiling the plane, normal tiling.
@article{SEMR_2017_14_a66,
author = {O. G. Bagina},
title = {The properties of mosaic pentagons with a pair of equal adjacent edges},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {1380--1412},
publisher = {mathdoc},
volume = {14},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a66/}
}
O. G. Bagina. The properties of mosaic pentagons with a pair of equal adjacent edges. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1380-1412. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a66/