I’m using the term “cubish polyhedra” here to refer to polyhedra which resemble a cube, if one looks only at the faces they have which feature the largest number of sides, always six in number, and with positions corresponding to the faces of a cube. In the first two examples shown, these faces are 36-sided polygons, also known as triacontakaihexagons. (Any of the images in this post may be enlarged with a click.)
Polyhedra fitting this description have appeared on this blog before, but it had not occurred to me to name them “cubish polyhedra” until today. The next two shown have icosakaioctagons, or 28-sided polygons, as their six faces which correspond to those of a cube. Also, and unlike the triacontakaihexagons in the first two cubish polyhedra above, these icosakaioctagons are regular.
The next two cubish polyhedra shown feature, on the left, six hexadecagons (16 sides per polygon) for “cubish faces,” which are shown in yellow — and on the right, six dodecagons (12 sides each), shown in orange. This last one, with the dodecagons, is unusual among cubish polyhedra in that all of its other faces are pentagons.
All six of these cubish polyhedra were made using Stella 4d: Polyhedron Navigator, a program you can find right here.