Applet below shows central cross sections of 16-cells and 28-cells 4-dimensional antiprism (separately)from lower to upper base (for definition and basic description see a page of 'Literka': 4-dimensional antiprisms.. As it is written there 16-cells antiprism is a regular 16-cells polytope) Click on a label "... cells" to change viewing animation.
To get basic ideas about 3-dimensional antiprisms see 3-dimensional antiprisms.
Pictures of the applet below are interesting for another reason. They present polyhedrons morphing. For 16-cells polytope we begin with a regular tetrahedron transforming into 14-faces semi-regular polyhedron, then back to a regular tetrahedron.
In the second case (28-cells polytope) we begin with regular hexahedron, then semi-regular polyhedron with 26 faces, then regular octahedron.