Snub DisphenoidA vertex-turning Snub Disphenoid which is Johnson solid #84.
Soph's DiamondThe Curvy Copter Plus in shape of a hexagonal dipyramid.
Spax DiamondA Spax Cube redesigned to have the shape of a hexagonal dipyramid
StinxA megaminx with one layer removed. Only six sides are twistable.
SunshineA corner turning triakis tetrahedron that is equivalent to a corner turning hexahedron with non-equidistant cuts.
Tera-IcosamoidA bandaged and heavily truncated Teraminx, although this was not the inventor's intention.
TeramoidThe even higher-order version of the megamoid
Triakis PyraminxA pyraminx truncated and extended again to give it the incomplete shape of a triakis tetrahedron.
Triakis SkewbA skewb in shape of a triakis tetrahedron which is a catalan solid.