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Dual polyhedron: Quiz


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.
Partially ordered setOrder theoryTotal orderBinary relation

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

Question 3: n-________ family {4,3,...,3,4}
Octeractic honeycombHepteractic honeycombHypercubic honeycombPenteractic honeycomb

Question 4: A self-dual 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.
Conic sectionProjective geometryProjective spaceAlgebraic geometry

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

Question 7: Such a poset may be represented in a ________.
Hasse diagramEquivalence relationOrder theoryPartially ordered set

Question 8: For example, in four dimensions, the vertex figure of the 600-cell is the ________; the dual of the 600-cell is the 120-cell, 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 self-dual.
Great icosahedronSmall stellated dodecahedronGreat stellated dodecahedronKepler–Poinsot polyhedron

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.
IcosahedronUniform polyhedronUniform polychoronDodecahedron


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