GeoGebra

Convex Hexagon Tessellations

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In 1918, K. Reinhardt (Über die Zerlegung der Ebene in Polygone, Inaugural-Disstertation, Univ. Frankfurt a.M., R. Noske, Borna and Leipzig) showed that there are only three types of convex hexagons which can be the tile in a monohedral (one-tile) tessellation:

250px 250px 250px
Ggb.gif Hexagons-I.ggb
Type 1
B + C + D = 360°
A + E + F = 360°
a = d
Ggb.gif Hexagons-II.ggb
Type 2
A + B + D = 360°
C + E + F = 360°
a = d
c = e
Ggb.gif Hexagons-III.ggb
Type 3
A = C = E = 120°
a = a'
c = c'
e = e'

These GeoGebra files each show a small portion of the Type 1, 2, and 3 tessellations, and allow you to change the angles and sides of the base hexagon.