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Leonardo polyhedron
A polyhedron with many holes From Wikipedia, the free encyclopedia
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Leonardo polyhedron is a polyhedron with a Platonic solid's rotational symmetry and has genus . Here, a polyhedron is the unbounded 2-manifold embedded in three-dimensional Euclidean space. The polyhedron is named after Leonardo da Vinci, who illustrated geometrical shapes in Luca Pacioli's De divina proportione in three phases: drawing Platonic solids and Archimedean solids; replacing the edges of those solids by struts, forming a convex polygon, and this results in the first polyhedron with many genera; and placing each hole with the skeleton of a pyramid.[1]

Alicia Boole Stott discovered the first regular Leonardo polyhedron (its property has transitivity by the set consisting of vertex, edge, and face of a polyhedron). Similar to Leonardo's work, she began the construction with a four-dimensional polytope, projecting to a Schlegel diagram, and replacing its edges with quadrilateral-shaped struts.[2] Coxeter later discovered the regular skew polyhedron.[3] Felix Klein discovered the three genera.[4] Together with Robert Fricke, they found the five genera of Leonardo polyhedra.[5] Some colleagues further discovered the locally regular and the genus up to 14.[6]
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