Instead of looking at the rolling thing itself, we can look at its foot-print on the ground.

In 3d, the ground is 2d. A cylinder laid on the ground produces a line, and rolling this cylinder moves the line across the plane, vertical to the line. Motor-car wheels are short lines that are easy to change the direction of motion. Stood on its end, the ground-section becomes a circle, and the thing does not roll.

A sphere produces a point, and this is perfectly capable of rolling in a great variety of directions.

A cone produces a line, but this line acts as a radius of a circle.

In 4d, the ground is 3d. So if the section is 2d, it rolls perpendicular to that. A 1d section gives a two-directional movement, and a point gives a 3d range. Such are the outcome when the vertical section of the prism is a circle, sphere, and glome. Note that the floor of a car cabin would be the 2d section times the forward motion. So in the case of a duocylinder, the cab becomes a cylinder-section, the foot-print is the end of such, we don't want the occupants to get giddy, so we should not rotate the non-rolling part of the cylinder.

A swirl-prism has a foot-print in the shape of one of its faces, such as a pentagon. Under rotation, the pentagon advances on the ground vertical to its hedrix (2space), but in the process, it rotates. The whole swirl-prism is rotating, which means that if drive is passed across another face of the swirlprism, it would turn the 'wheel' at a 1:1 ratio of the drive. The cabin would need to be supported on a different set of bearings, but such bearings, breaks etc, can be applied to a surface different to the one that contacts the ground.

The spheric pyramid still presents a line, but the rotation becomes the radius of a sphere.

The bicircular tegum presents a line, this can freely move around, because the two different ends can be advanced at different speeds.

A sphere-line cone (ie a cone-pyramid), produces a triangular foot, one side is stationary, while the other can rotate around it.