##  [Nonmanifold Vertex](/index.php/nonmanifold-vertex) 

  ##  [Nonmanifold Vertex](https://puremath.quantumdictionary.io/nonmanifold-vertex-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A vertex in a polyhedral or simplicial complex whose incident faces or higher-dimensional cells fail to form a neighborhood homeomorphic to a ball (or half-ball), so the manifold condition is violated at that point and the local topology is singular.