Uniform polyhedron
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In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive. It follows that all vertices are congruent.
Platonic solid: Tetrahedron
Image: Tetrakishexahedron
Image: Disdyakisdodecahedron
Image: Disdyakistriacontahedron
Semiregular polyhedron
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In geometry, the term semiregular polyhedron is used variously by different authors.
Image: Rhombicdodecahedron