from III - Polytopes of Nearly Full Rank
Published online by Cambridge University Press: 30 January 2020
As in the case of the 3-dimensional regular apeirohedra described in the previous chapter, the mirror vector plays an important role in the classification of the 4-dimensional regular polyhedra. Thus the first task is to determine the possible mirror vectors of such polyhedra. The polyhedra with mirror vector (3,2,3) and their relatives under standard operations such as Petriality form a specially rich family. One particular family of these polyhedra is treated in detail, with a description of their realization domains. With the mirror vector (2,3,2), most of the standard operations lead to polyhedra in the same class. Though there is a close analogy between the infinite and finite cases, those with mirror vector (2,2,2) have symmetry groups that need not be related to reflexion groups; the treatment here employs quaternions. There are various connexions among these regular polyhedra, the most interesting being the way that the skewing operation takes certain polyhedra in class (3,2,3) into polyhedra of class (2,2,2).
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.