On the Chromatic Number of $$\mathbb {R}^4$$ R 4

The lower bound for the chromatic number of $$\mathbb {R}^4$$R4 is improved from $$7$$7 to $$9$$9. Three graphs with unit distance embeddings in $$\mathbb {R}^4$$R4 are described. The first is a $$7$$7-chromatic graph of order $$14$$14 whose chromatic number can be verified by inspection. The second is an $$8$$8-chromatic graph of order $$26$$26. In this case the chromatic number can be verified quickly by a simple computer program. The third graph is a $$9$$9-chromatic graph of order $$65$$65 for which computer verification takes about one minute.