Could pentaprisms have an interesting property in the fourth dimension?

A pentaprism is a five-sided reflecting prism used to deviate a beam of light by a constant 90°, even if the entry beam is not at 90° to the prism. The beam reflects inside the prism twice, allowing the transmission of an image through a right angle without inverting it (that is, without changing the image's handedness) as an ordinary right-angle prism or mirror would.

I was thinking that it is an efficient way of giving light chirality in higher dimensions just like hexagons are efficient at filling space in two dimensions.