Portraits of a Family of Complex Polytopes

@article{Coxeter1993PortraitsOA,
  title={Portraits of a Family of Complex Polytopes},
  author={H. S. M. Coxeter and Geoffrey C. Shephard},
  journal={Leonardo},
  year={1993},
  volume={25},
  pages={239 - 244}
}
Regular complex polytopes in unitary space have been studied since the 1950s. The advent of computer graphics has enabled us to represent these on the real plane in a meaningful way with very little effort. Here we are chiefly concerned with a particular sequence of complex polytopes in two, three and four dimensions and with some associated real polytopes. 

Reciprocating the Regular Polytopes

For reciprocation with respect to a sphere ∑x2=c in Euclidean n‐space, there is a unitary analogue: Hermitian reciprocation with respect to an antisphere ∑ūu=c. This is now applied, for the first

Cartography of Tree Space

How can vibrant, contemporary art be produced that deals with vibrant, contemporary mathematics? To address this question, a collaboration began between an artist (Schuh) and a mathematician

Parity proofs of the Kochen–Specker theorem based on the Lie algebra E8

A proof involving 34 rays and 9 bases appears to provide the most compact proof of the Kochen–Specker (KS) theorem found to date in eight-dimensions.

Coordinates for the Regular Complex Polygons

Certain projections of the real polytopes {3, 3, 4}, {3, 4, 3}, {3, 3, 5} suggest highly symmetric coordinates for the self‐reciprocal complex polygons 3{3}3, 4{3}4, 3{4}3, 5{3}5 and 3{5}3. Although

Morphophoric POVMs, generalised qplexes, and 2-designs

The primal equation of QBism designed for SIC-POVMs is extended to the morphophoric case, and generalised qplexes generated by MUB-like 2-design POVMs utilising their graph-theoretical properties are examined.

Generalised qplexes, similarity to quantum state space, and 2-designs

We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to

Morphophoric POVMs, generalised qplexes,ewline and 2-designs

We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to

References

SHOWING 1-7 OF 7 REFERENCES

The equianharmonic surface and the Hessian polyhedron

SummaryThis paper develops a new approach to B. Segre's symmetric notation for the 27 lines on a cubic surface, and a presentation for the group of automorphisms of the Pappus configuration 93.

The Pure Archimedean Polytopes in Six and Seven Dimensions

An Archimedean solid (in three dimensions) may be defined as a polyhedron whose faces are regular polygons of two or more kinds and whose vertices are all surrounded in the same way. For example, the

Hypergraphs and abstract polygons

The notion of a graph has recently been generalized to include structures called hypergraphs which have two or more vertices per edge. A hypergraph is called 2-settled if each pair of distinct

Coxcter, Regular Complex Polytopes, 2nd Ed

  • 1991

Regular Complex Polytopes