Update of 9:29 PM ET Dec. 20, 2017 —
See in particular, in the above Notices , the article
"Algebraic Structures on Polytopes," by Federico Ardila,
within the 2018 Joint Mathematics Meeting Lecture Sampler.
Related reading:
arXiv:1711.09102v1 [hep-th] 24 Nov 2017,
"Scattering Forms and the Positive Geometry of
Kinematics, Color and the Worldsheet," by
Nima Arkani-Hamed, Yuntao Bai, Song He, Gongwang Yan
(Submitted to the arXiv on 24 Nov. 2017).