It was discovered by Thorold Gosset with his 1900 paper of semiregular polytopes.
It can be seen as an alternation of a truncated 24-cell honeycomb, and can be represented by Schläfli symbol s{3,4,3,3}, s{31,1,1,1}, and 3 other snub constructions.
It is defined by an irregular decachoron vertex figure (10-celled 4-polytope), faceted by four snub 24-cells, one 16-cell, and five 5-cells.
The vertex figure can be seen topologically as a modified tetrahedral prism, where one of the tetrahedra is subdivided at mid-edges into a central octahedron and four corner tetrahedra.
Each symmetry can be represented by different arrangements of colored snub 24-cell, 16-cell, and 5-cell facets.