---
tag: EFV05HMXPG
kind: concept
name: Laves graph
aliases: [diamond-twin, k4-crystal, laves-lattice]
sources:
  - wikipedia: en:44557148@r1368660653
    locator: Laves graph
    note: adopted
    mention: wikipedia://en/44557148
    sections: [Summary]
same_as:
  wikidata: Q25303739
  wikipedia: Laves graph
inventory: [J2B6X7EVBE]
---

## Summary

In geometry and crystallography, the **Laves graph** is an infinite and highly symmetric system of points and line segments in three-dimensional [[Euclidean space|0XPR1E85W0]], forming a periodic graph. Three equal-length segments meet at 120° angles at each point, and all cycles use ten or more segments. It is the shortest possible triply periodic graph, relative to the volume of its fundamental domain. One arrangement of the Laves graph uses one out of every eight of the points in the integer lattice as its points, and connects all pairs of these points that are nearest neighbors, at distance $\sqrt2$. It can also be defined, divorced from its geometry, as an abstract undirected graph, a covering graph of the [[complete graph|03WKB2H474]] on four vertices.