The wheel graph  can be realized as a strict unit distance graph with six of its vertices forming a unit regular hexagon and the seventh at the center of the hexagon. Removing one of the edges from the center vertex produces a subgraph that still has unit-length edges, but which is not a strict unit distance graph.
The wheel graph can be described as a unit distance graph with six vertices forming a regular hexagon, and a seventh vertex at its center. Removing one edge from the central vertex creates a subgraph that still has edges of unit length but is not a strict unit distance graph.