Polygon Offset and Point and Lines
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Polygon offset, as its name implies, only works with polygonal primitives. It affects only the filled primitives: GL_TRIANGLES, GL_TRIANGLE_STRIP, GL_TRIANGLE_FAN, GL_QUADS, GL_QUAD_STRIP, and GL_POLYGON. Polygon offset will work when you render them with glPolygonMode set to GL_FILL, GL_LINE, or GL_POINT.
Polygon offset doesn't affect non-polygonal primitives. The GL_POINTS, GL_LINES, GL_LINE_STRIP, and GL_LINE_LOOP primitives can't be offset with glPolygonOffset().