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There are 13 polyhedra with two or more regular polygons as their faces. Called the "Archimedean
solids," each has a dual called a "Catalan solid," in which vertices are replaced by faces and faces become
vertices. Although there is an Archimedean solid (truncated icosidodecahedron) with 120 vertices, there are no
Archimedean or Catalan solids with 144 vertices. This means that the 264 yods in the seven enfolded polygons cannot
symbolize vertices of one or more polyhedra. Although there is a Catalan solid with 120 faces, there are no
Archimedean or Catalan solids with 144 faces. The disdyakis triacontahedron is this Catalan solid with the most
faces. However, the Catalan solid called the "disdyakis dodecahedron" has **48** triangular
faces. Sticking tetrahedra on its faces creates a required polyhedron with 144 faces. Adding square pyramids with
four faces to an Archimedean or a Catalan solid cannot create such a polyhedron because there is none that has
**36** faces. Only one member of the **26** Archimedean & Catalan solids
can therefore generate a polyhedron with 144 faces. The disdyakis dodecahedron has
**26** vertices, **72** edges & **48** faces. Adding
tetrahedra to the latter creates a polyhedron with (**26**+**48**=74) vertices,
(**72** + 3×**48** = **216**) edges and
(**48**×3=144) triangular faces. This will be called the "144 Polyhedron."

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