Punctured Polyhedra
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Ivars Peterson (MathTrek)  
A tetrahedron has four triangular faces, four vertices, and six edges. When a vertex of one tetrahedron pierces the face of a second tetrahedron it forms a new, more complicated polyhedron: one triangular face has a triangular "hole" where the face was pierced. Mathematicians describe such a punctured face as being "multiply connected." Several years ago, mathematician John H. Conway wondered whether a polyhedron could have such a polygonal hole passing through each and every face and remain a polyhedron. He coined the term "holyhedron" to describe this form, should it exist... Jade Vinson's surprising solution is now slated for publication in the journal Discrete and Computational Geometry.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles 
Math Topics:  Computational Geometry, HigherDimensional Geometry, Polyhedra 
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