"""
Coxeter Matrix for H4 in Coxeter3:
[1 5 2 2]
[5 1 3 2]
[2 3 1 3]
[2 2 3 1]
"""

"""
The set of all elements in H4 that are fully-commutative but not subregular
form a single 2-sided cell. It contains 162 elements. All elements in it have
a-value 2.
""" 

fccox = {13,14,24,124,132,134,143,213,214,243,324,1213,1214,1243,1321,1324,1432,2124,2132,2134,2143,3214,3243,12124,12132,12134,12143,13212,13214,13243,14321,21213,21214,21243,21321,21324,21432,32124,32143,121243,121321,121324,121432,132123,132124,132143,143212,212132,212134,212143,213212,213214,213243,214321,321213,321214,321243,321432,1213212,1213214,1213243,1214321,1321234,1321243,1321432,1432123,2121321,2121324,2121432,2132123,2132124,2132143,2143212,3212132,3212134,3212143,3214321,4321213,12132123,12132124,12132143,12143212,13214321,14321234,21213212,21213214,21213243,21214321,21321234,21321243,21321432,21432123,32121321,32121324,32121432,32143212,43212132,43212134,121321234,121321243,121321432,121432123,132143212,212132123,212132124,212132143,212143212,213214321,214321234,321213212,321213214,321213243,321214321,321432123,432121321,432121324,1213214321,1214321234,1321432123,2121321234,2121321243,2121321432,2121432123,2132143212,3212132123,3212132124,3212132143,3212143212,3214321234,4321213212,4321213214,4321213243,12132143212,13214321234,21213214321,21214321234,21321432123,32121321234,32121321243,32121321432,32121432123,43212132123,43212132124,43212132143,121321432123,212132143212,213214321234,321213214321,321214321234,432121321234,432121321243,432121321432,1213214321234,2121321432123,3212132143212,4321213214321,21213214321234,32121321432123,43212132143212,321213214321234,432121321432123,4321213214321234}

""" 
This 2-sided cell splits into left cells. 
"""

l1cox =  {13,143,213,1213,2143,12143,21213,32143,132143,212143,321213,2132143,3212143,4321213,12132143,212132143,3212132143,43212132143}
l2cox =  {14,134,214,1214,2134,3214,12134,13214,21214,212134,213214,321214,1213214,3212134,21213214,43212134,321213214,4321213214}
l3cox =  {24,124,324,1324,2124,12124,21324,32124,121324,132124,2121324,2132124,12132124,32121324,212132124,432121324,3212132124,43212132124}
l4cox =  {132,1432,2132,12132,21432,121432,212132,321432,1321432,2121432,3212132,21321432,32121432,43212132,121321432,2121321432,32121321432,432121321432}
l5cox =  {243,1243,3243,13243,21243,121243,213243,321243,1213243,1321243,21213243,21321243,121321243,321213243,2121321243,4321213243,32121321243,432121321243}
l6cox =  {1321,14321,21321,121321,214321,1214321,2121321,3214321,13214321,21214321,32121321,213214321,321214321,432121321,1213214321,21213214321,321213214321,4321213214321}
l7cox =  {13212,143212,213212,1213212,2143212,12143212,21213212,32143212,132143212,212143212,321213212,2132143212,3212143212,4321213212,12132143212,212132143212,3212132143212,43212132143212}
l8cox =  {132123,1432123,2132123,12132123,21432123,121432123,212132123,321432123,1321432123,2121432123,3212132123,21321432123,32121432123,43212132123,121321432123,2121321432123,32121321432123,432121321432123}
l9cox = {1321234,14321234,21321234,121321234,214321234,1214321234,2121321234,3214321234,13214321234,21214321234,32121321234,213214321234,321214321234,432121321234,1213214321234,21213214321234,321213214321234,4321213214321234}
