# 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.

## 9 Citations

### Reciprocating the Regular Polytopes

- Mathematics
- 1997

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

- ArtLeonardo
- 2019

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

- Mathematics, Computer Science
- 2015

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

- Mathematics
- 1997

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

- MathematicsQuantum
- 2020

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

- Mathematics
- 2019

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

- Mathematics
- 2020

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…

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