I believe this is the disphenoidal 288-cell. A spherical code that combines two 24-cells has the same minimal Euclidean distance as the vertices of the 288-cell, and those same vertices form the 2O group when written as unit quaternions. See http://errorcorrectionzoo.org/c/disphenoidal288cell for references.

I believe this is the disphenoidal 288-cell. A spherical code that combines two 24-cells has the same minimal Euclidean distance as the vertices of the 288-cell, and those same vertices form the 2O group when written as unit quaternions. See https://errorcorrectionzoo.org/c/disphenoidal288cell for references.