# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Friday, June 18, 2004, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Jiří Matoušek (Charles Univ.)

## Simplex Reptiles Could Help the Net Police, But Probably They Do Not Exist

A polyhedron *P* in *R*^{d} is called a *k*-reptile if *P* can be tiled without
overlaps by *k* similar copies of itself that are all congruent (*k>1*).
For example, the right isoceles triangle in the plane is a 2-reptile.
I will (try to) prove that for *d>2* there are no *d*-dimensional simplices
that are 2-reptiles. It seems plausible, but maybe hard to prove,
that if a *d*-simplex is a *k*-reptile, *d>2*, then *k* must be at least *2*^{d}.
This (very incomplete) investigation has been motivated by probabilistic
encoding of the routes of messages on the Internet.

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