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Uniform polychoron: Quiz


Question 1: See also ________, some of which illustrate these operations as applied to the regular cubic honeycomb.
OctahedronCubeConvex uniform honeycombUniform polychoron

Question 2:
  • 1910: Alicia Boole Stott, in her publication Geometrical deduction of semiregular from regular polytopes and space fillings, expanded the definition by also allowing ________ and prism cells.
    Uniform polyhedronArchimedean solidPolyhedronRhombicosidodecahedron

Question 3: 9 are in the self-dual regular A4 [3,3,3] group (________) family.

Question 4: The other forty can be derived from the regular polychora by geometric operations which preserve most or all of their ________, and therefore may be classified by the symmetry groups that they have in common.
Group (mathematics)Euclidean groupSymmetry (physics)Symmetry

Question 5: Elte expanded on Gosset's work with the publication The Semiregular Polytopes of the Hyperspaces, including a special subset of polytopes with semiregular facets (those constructible by a single ringed node of a ________).
HypercubeCross-polytopeUniform polychoronCoxeter–Dynkin diagram

Question 6: 5 are polyhedral prisms based on the ________ (1 overlap with regular since a cubic hyperprism is a tesseract)
IcosahedronTetrahedronDodecahedronPlatonic solid

Question 7:
  • 1900: Thorold Gosset enumerated the list of nonprismatic semiregular convex polytopes with regular cells (________) in his publication On the Regular and Semi-Regular Figures in Space of n Dimensions.
    TetrahedronIcosahedronDodecahedronPlatonic solid

Question 8: The second is the infinite family of uniform duoprisms, products of two ________.
HexagonRegular polygonOctagonPentagon

Question 9: In ________, a uniform polychoron (plural: uniform polychora) is a polychoron or 4-polytope which is vertex-transitive and whose cells are uniform polyhedra.
ManifoldMathematicsAlgebraic geometryGeometry

Question 10: 1 special snub form in the [3,4,3] group (________) family.


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