These shapes together with pentagons make up the sides of a truncated icosahedron [ie-KOE-suh-hee-dron], and this shape, triangles, and squares are the only regular figures that can tessellate a plane.
If segments are added connecting consecutive midpoints of the sides of one of these regular polygons, the new similar polygon has three-fourths the area of the original. These shapes together with pentagons make up the sides of a truncated icosahedron [ie-KOE-suh-hee-dron], and this shape, triangles, and squares are the only regular figures that can tessellate a plane. The length of this shape's apothem [ah-POTH-um] equals its side length times one-half times the square root of three. Name these polygons with six sides.
If segments are added connecting consecutive midpoints of the sides of one of these regular polygons, the new similar polygon has three-fourths the area of the original.
(regular) hexagon (prompt on "6-gon")