The Grötzsch graph is the smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph with index four. It has 11 vertices, 20 edges, and graph crossing number 5. It is Hamiltonian, but nonplanar. It is illustrated above in a number of drawings.
The plots above show the adjacency matrix, incidence matrix, and graph distance matrices for the Grötzsch graph.
The graph spectrum of the Grötzsch graph is 
.
de Grey (2026) considered a unit-distance embedding of the Grötzsch graph in three dimensions in his construction
of a triangle-free graph that is a unit-distance
graph in 
with chromatic number 5, though ended up using
a different graph on 31 vertices.
The unit-distance embedding considered
by de Grey, together with a similar one based on a pentagram
instead of a pentagon, is illustrated above.
The Grötzsch graph is implemented in the Wolfram Language as GraphData["GroetzschGraph"].
With 61 Vertices." Geombinatorics 35,
2026.House of Graphs. "Groetzsch Graph." 
th
Chromatic Numbers of the Grötzsch Graph." J. Graph Th. 21,
207-209, 1996.