It derives ultimately from the Latin for "four". The chain goes something like
Latin quattour "four"
Latin quadrus "square"
Latin exquadrare "to make square"
Old French esquire "a square, squareness"
English square
square= 'four equal'
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Square.
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Square
the vertices are the corners to the shape, so you count the corners to whatever shape.
There are several names for a 26 sided shape, they are: Elongated Square Gyrobicupola, Rhombicuboctahedron, Snub Square Antiprism, the Great Rhombcuboctahedron, and a 26-agon. The suggested name of a 26 sided shape is Icosikaihexagon.