Question 1: An abstract polyhedron is a certain kind of ________ (poset) of elements, such that adjacencies, or connections, between elements of the set correspond to adjacencies between elements (faces, edges, etc.) of a polyhedron.  

Question 2: We can distinguish between structural (________) duality and geometrical duality.  

Question 3: n________ family {4,3,...,3,4}  

Question 4: A selfdual polyhedron is a ________ whose dual is a congruent figure, though not necessarily the identical figure: for example, the dual of a regular tetrahedron is a regular tetrahedron "facing the opposite direction" (reflected through the origin).  

Question 5: The concept of duality here is closely related to the duality in ________, where lines and edges are interchanged; in fact it is often mistakenly taken to be a particular version of the same.  

Question 6: In ________, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.  

Question 7: Such a poset may be represented in a ________.  

Question 8: For example, in four dimensions, the vertex figure of the 600cell is the ________; the dual of the 600cell is the 120cell, whose facets are dodecahedra, which are the dual of the icosahedron.  

Question 9: So the regular polyhedra — the Platonic solids and ________ — are arranged into dual pairs, with the exception of the regular tetrahedron which is selfdual.  

Question 10: For a ________, the face of the dual polyhedron may be found from the original polyhedron's vertex figure using the Dorman Luke construction.  

