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A dodecahedron.
A polyhedron with 12 congruent faces is a dodecahedron.
Using Euler's Polyhedron formula V+F-E=2, givenF=14 and E=24, we have V=12.The polyhedron has 12 vertices.This assumes a genus-0 polyhedron. An example would be the hexagonal antiprism, a polyhedron having two hexagonal faces and 12 triangular faces.
WHAT IS A SOLID WITH TWELVE faces and 30 edgesis a dodecahedron.
It has 6 vertices.