----------------------------- Possible Legal Cross Patterns ----------------------------- Plummer Cross (6 Cross order 3) = 8 patterns Christman Cross (6 Cross order 2) = 6 patterns 4 Cross order 2 (sq group) = 3 patterns 4 Cross order 4 = 6 patterns ----------- 14 Six Cross + 9 Four Cross = 23 total legal Cross patterns
There are 0 total cross patterns in the swap orbit
------------------------- Possible Legal X Patterns ------------------------- 6 X order 3 = 8 patterns 6 X order 6 = 8 patterns 6 X order 2 (sq group) = 1 pattern 4 X order 2 (sq group) = 3 patterns 2 X order 2 (sq group) = 3 patterns ----------- 17 Six X + 3 Four X + 3 Two X = 23 total legal X patterns
For a while I thought that [6 x order 3] combined with the [2 x pattern]
would make a new sort of [6 x order 6], but combining [6 x order 3] with
the [2 x pattern] is essentially the same as combining 6 x order 3 with
the pons asinorum or 6 x order 2.
------------------------------ Possible Swap-Orbit X Patterns ------------------------------ 6 X order 2 = 6 patterns 6 X order 4 = 6 patterns 4 X order 2 = 6 patterns 4 X order 4 = 6 patterns -----------
12 Six X + 12 Four X = 24 total swap-orbit X patterns
Some description of the swap-orbit patterns is in order.
The 6 X order 2 pattern has a 2-cycle of opposite edges and
2 sets of 2-cycles of adjacent edges.
The 6 X order 4 pattern has a 2-cycle of opposite edges and
a 4-cycle of edges of adjacent faces.
The 4 X order 2 has 2 sets of 2-cycles of adjacent edges.
The 4 X order 4 has a 4-cycle of edges of adjacent faces.
To make any of these swap-orbit patterns one would have to first
exchange any 2 edge cubies.
Interestingly, a thin line 6 X order 3 is possible on the 5x5x5
cube. No process as yet....
-> Mark <-
Email: mark.longridge@canrem.com