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----------------------------- 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