# Hyperideal polyhedra in the 3-dimensional anti-de Sitter space

## TL;DR

This paper investigates hyperideal polyhedra in 3D anti-de Sitter space, establishing their unique determination by combinatorics, dihedral angles, and boundary metrics, and characterizing the possible geometric configurations.

## Contribution

It provides a comprehensive description of hyperideal polyhedra in AdS3, including uniqueness results and conditions for dihedral angles and boundary metrics.

## Key findings

- Hyperideal polyhedra are uniquely determined by combinatorics and dihedral angles.
- The paper characterizes possible dihedral angles for hyperideal polyhedra.
- It describes the induced boundary metrics and their relation to the polyhedra's geometry.

## Abstract

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space $AdS^3$, which are defined as the intersection of the projective model of $AdS^3$ with a convex polyhedron in $RP^3$ whose vertices are all outside of $AdS^3$ and whose edges all meet $AdS^3$. We show that hyperideal polyhedra in $AdS^3$ are uniquely determined by their combinatorics and dihedral angles, as well as by the induced metric on their boundary together with an additional combinatorial data, and describe the possible dihedral angles and the possible induced metrics on the boundary.