The Euler-Schlaefli Equation

Loeb, Arthur L.

doi:10.1007/978-1-4612-0437-4_3

Arthur L. Loeb³

Part of the book series: Design Science Collection ((DSC))

346 Accesses

Abstract

In 1752 Leonhard Euler formulated a relationship between the numbers of elements of different dimensionality in a structure, which was generalized very elegantly by Schlaefli exactly one hundred years later. Schlaefli put his relationship in the following form:

$$ \mathop \sum \limits_{i = 0}^j ( - 1)^i N_i = 1 + ( - 1)^j $$

(3-1)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Softcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Department of Visual and Environmental Studies, Carpenter Center for the Visual Arts, Harvard University, Cambridge, MA, 02138, USA
Arthur L. Loeb

Authors

Arthur L. Loeb
View author publications
You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Loeb, A.L. (1991). The Euler-Schlaefli Equation. In: Space Structures. Design Science Collection. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0437-4_3

Download citation

DOI: https://doi.org/10.1007/978-1-4612-0437-4_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6759-1
Online ISBN: 978-1-4612-0437-4
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics