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It is possible, but not necessary. A hexagon can have 0, 2, 3, 4, 5, or 6 parallel sides. A regular hexagon has 3 parallel sides.
False.
Shapes can tessellate only if a number of them can meet at a point and cover 360 degrees without overlap. For regular shapes this requires that the angles of the shape are a factor of 360 degrees. For non-regular shapes it is necessary that the angles of the shapes can be grouped so that they sum to 360 degrees.
a triangle is not regular
A regular hexahedron.A regular hexahedron.A regular hexahedron.A regular hexahedron.