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You asked:

what are the types of polyhedrons

  • Polyhedron's subclasses include icosahedron, prism, square pyramid, Triangular dipyramid and Pentagonal dipyramid.
  • prism
    prism
    prism

    prism (a polyhedron with two congruent and parallel faces (the bases) and whose lateral faces are parallelograms)

  • Triangular dipyramid
    Triangular dipyramid
    Triangular dipyramid

    triangular dipyramid, a first in the infinite set of face-transitive dipyramids

  • Pentagonal dipyramid
    Pentagonal dipyramid
    Pentagonal dipyramid

    pentagonal dipyramid, third of the infinite set of face-transitive dipyramids

  • Net
    Net
    Net

    arrangement of edge-joined polygons in the plane which can be folded to become the faces of the polyhedron

  • Pentahedron
    Pentahedron
    Pentahedron

    pentahedron, a polyhedron with five faces

  • Deltoidal hexecontahedron
    Deltoidal hexecontahedron
    Deltoidal hexecontahedron

    deltoidal hexecontahedron, a catalan solid which looks a bit like an overinflated dodecahedron

  • gyroelongated pentagonal pyramid
    gyroelongated pentagonal pyramid
    gyroelongated pentagonal pyramid

    gyroelongated pentagonal pyramid, one of the Johnson solids

  • Pentagonal icositetrahedron
    Pentagonal icositetrahedron
    Pentagonal icositetrahedron

    pentagonal icositetrahedron, a catalan solid which is the dual of the snub cube

  • Disdyakis triacontahedron
    Disdyakis triacontahedron
    Disdyakis triacontahedron

    disdyakis triacontahedron, or hexakis icosahedron, a Catalan solid and the dual to the Archimedean truncated icosidodecahedron

  • Disdyakis dodecahedron
    Disdyakis dodecahedron
    Disdyakis dodecahedron

    disdyakis dodecahedron, or hexakis octahedron, a Catalan solid and the dual to the Archimedean truncated cuboctahedron