# Geometric criteria for realizability of tensegrities in higher dimensions

## TL;DR

This paper provides geometric criteria for determining when tensegrity frameworks in higher dimensions can have self-stresses, using Grassmann-Cayley algebra and discrete forms.

## Contribution

It offers a complete set of geometric conditions for the realizability of certain tensegrities in any dimension, connecting algebraic and geometric perspectives.

## Key findings

- Characterization of self-stresses in $(d+1)$-valent tensegrities
- Use of Grassmann-Cayley algebra to formulate conditions
- Link between discrete multiplicative 1-forms and geometric realizability

## Abstract

In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities. We give a complete answer on geometric conditions of at most $(d+1)$-valent tensegrities in $\mathbb{R}^d$ both in terms of discrete multiplicative 1-forms and in terms of "meet" and "join" operations in the Grassmann-Cayley algebra.