Answer:

EDGES

Answer	Crossword Clue
EDGES	Dagger's pair
EDGES	Margins of superiority
EDGES	Trims

EDGES	Competitive advantages
EDGES	Noses (out)
EDGES	Rims
EDGES	Extremities
EDGES	Periphery
EDGES	Advantages
EDGES	Borders
EDGES	Peripheries

EDGES	Cubes have 12, spheres none
EDGES	Perimeter formers
EDGES	Perimeters
EDGES	Just beats
EDGES	Squeezes (past)
EDGES	Boundaries
EDGES	Cube's dozen
EDGES	Barely beats

EDGES	Beats by a bit
EDGES	Margins
EDGES	Beats by a little
EDGES	Does lawn work
EDGES	Blades' sharp sides
EDGES	Finishes, as a lawn
EDGES	Pieces jigsaw puzzlers usually start with
EDGES	Beats 1-0, say

EDGES	Beats by a nose
EDGES	They may be rough
EDGES	Beats by a hair
EDGES	A cube has twelve
EDGES	Outer limits
EDGES	Noses out
EDGES	Cubes have twelve
EDGES	Cutting sides

EDGES	Lips
EDGES	Sharpens
EDGES	Barely wins, with "out"
EDGES	A pyramid has six
EDGES	Fringe areas