Augmenting the stellatruncated cube

The stellatruncated cube, vertex figure (8/3,8/3,3)

Left: Each octagrammic face of the stellatruncated cube can be excavated with an octagrammic pyramid completing a cycle around the axis.  The 8/3 in the vertex figure is replaced by a (3,3)   The original vertex figures become (3,3,3,3,3)/2 with new vertices of (3,3,3,3,3,3,3,3)/3 - or (38)/3.  This is a unique case where the original triangular faces are left in place while all other faces are excavated.  The excavations are deep enough that the original triangular faces do not disrupt the local convexity of the vertices (diagram).  The faces of the pyramids are shown in yellow with the original triangles in blue.  All vertices lie on the convex hull.

Centre: Another augmentation of the stellatruncated cube has in addition to the octagrammic pyramids above, each triangular face also excavated with a triangular pyramid or tetrahedron completing a cycle around the axis.  The 3 in the original vertex figure is replaced by a (3,3)   The original vertex figures become (3,3,3,3,3,3)/2 with new vertices of (3,3,3,3,3,3,3,3)/3 - or (38)/3 and (3,3,3).  The faces of the octagrammic pyramids are shown in yellow with the tetrahedral faces in blue.  All vertices are on the exterior of the figure.

Right: A further augmentation of the stellatruncated cube can be obtained as follows:  Excavate one octagrammic cap of a crossed octagrammic antiprism with an octagrammic pyramid.  For brevity I refer to the resulting polyhedron as S8/5Y8/3.  This polyhedron is not locally convex but the act of joining it to the stellatruncated cube removes the retrograde polygon .  Excavate each of the octagrammic faces of the stellatruncated cube with an S8/5Y8/3.  The 8/3 in the vertex figure is replaced by a (3,3,3)/2   The original vertex figures become (3,3,3,3,3,3,3)/3 - or (37)/3 with new vertices from the S8/5Y8/3 of (3,3,3,3,3)/2 - or (35)/2 and (3,3,3,3,3,3,3,3)/3 - or (38)/3.  The original triangular faces of the stellatruncated cube are shown in blue, those of the anti-prisms in yellow and the pyramids pink.  All vertices lie on the convex hull.