Edge (geometry) definition

ecg. Cognate with German Ecke, Dutch egge, Swedish egg.

The boundary line of a surface.
The joining line between two vertices of a polygon.
The place where two faces of a polyhedron meet.
An advantage (as have the edge on)
The thin cutting side of the blade of an instrument; as, the edge of an ax, knife, sword, or scythe. Hence, figuratively, that which cuts as an edge does, or wounds deeply, etc.

He which hath the sharp sword with two edges. Rev. ii. 12.

Slander, \ Whose edge is sharper than the sword.
Any sharp terminating border; a margin; a brink; extreme verge; as, the edge of a table, a precipice.

Upon the edge of yonder coppice.

In worst extremes, and on the perilous edge \ Of battle. John Milton.

Pursue even to the very edge of destruction. Sir W. Scott.
Sharpness; readiness or fitness to cut; keenness; intenseness of desire.

The full edge of our indignation. Sir W. Scott.

Death and persecution lose all the ill that they can have, if we do not set an edge upon them by our fears and by our vices. Jeremy Taylor
The border or part adjacent to the line of division; the beginning or early part; as, in the edge of evening. "On the edge of winter." John Milton.
The edge of a cricket bat.
Any of the connected pairs of vertices in a graph.
In male masturbation, a level of sexual arousal that is maintained just short of reaching the point of inevitability, or climax.

To move an object slowly and carefully in a particular direction.

He edged the book across the table.
To move slowly and carefully in a particular direction.

He edged away from her.
(cricket) To hit the ball with an edge of the bat, causing a fine deflection.
Triming the margin of a lawn where the grass meets the sidewalk, usually with an electric or gas-powered lawn edger.

1925: Walter Anthony and Tom Reed (titles), Rupert Julian (director), The Phantom of the Opera, silent movie

In Mlle. Carlotta’s correspondence there appeared another letter, edged in black!