The Jørgensen graph is a maximally linklessly embeddable graph on 8 vertices and 21 edges, where "maximal" means it is not a proper subgraph of another linklessly embeddable graph of the same order (Jørgensen 1989, Naimi et al. 2020). It is illustrated above in a number of drawings.
The Jørgensen graph is implemented in the Wolfram Language as GraphData["JorgensenGraph"].
A family of maximally linklessly embeddable graphs on 
vertices and 
edges may be constructed
from this graph by subdividing
one of the horizontal edges and adding edges
that connect every new vertex to the top and bottom
vertices (Jørgensen 1989, Naimi et al.
2020).
." Report 1989: R 89-28. Aalborg, Denmark: Aalborg Universitetscenter,
Institut for Elektroniske Systemer, 1989.Naimi, R.; Pavelescu, A.; and
Pavelescu, E. "New Bounds on Maximal Linkless Graphs." 20 Sep 2020.