H4 (left) and H4Φ (right) 24-Cell
The left images are scaled up to the same size as the right image in order to show more detail. 
This accounts for the thicker edges and larger vertex shapes in the left image.
The light blue octahedron is the 8 vertex 16-cell.
The light red cube is the 16 vertex 8-cell (a Tesseract) with dual vertices at each corner. 
In these 3D projections of hyper-dimensional objects, we do not scale the 4th dimension as is sometime shown for the Tesseract.
All objects (above and below) use the same projection basis vectors. The only difference is in the selection from the 240 8D E8 vertices being projected.

ColumnForm[MatrixForm[{Row@{Column[{#,pDisp@#,pLbl@#},Center]}&/@#}]&/@{h4cell16,h4cell8,h4Φcell16,h4Φcell8}]

H4 (left) and H4Φ (right) Snub 24-Cell (1st of 4 rotations by (π/5) from the 0th rotation shown above)

ColumnForm[MatrixForm[{Row@{Column[{#,pDisp@#,pLbl@#},Center]}&/@#}]&/@{h4snub161,h4snub81,h4Φsnub161,h4Φsnub81}]

H4 (left) and H4Φ (right) Snub 24-Cell (2nd of 4 rotations by (π/5))

ColumnForm[MatrixForm[{Row@{Column[{#,pDisp@#,pLbl@#},Center]}&/@#}]&/@{h4snub162,h4snub82,h4Φsnub162,h4Φsnub82}]

H4 (left) and H4Φ (right) Snub 24-Cell (3rd of 4 rotations by (π/5))

ColumnForm[MatrixForm[{Row@{Column[{#,pDisp@#,pLbl@#},Center]}&/@#}]&/@{h4snub163,h4snub83,h4Φsnub163,h4Φsnub83}]

H4 (left) and H4Φ (right) Snub 24-Cell (4th of 4 rotations by (π/5))

ColumnForm[MatrixForm[{Row@{Column[{#,pDisp@#,pLbl@#},Center]}&/@#}]&/@{h4snub164,h4snub84,h4Φsnub164,h4Φsnub84}]