quickfur wrote:Klitzing wrote:And still I have to consider my own ideas: "Idea 3" was disproven, "idea 2" was elaborated. One of those 2 was definitely non-convex, as including stips for cells. So far I suppose that the other one so would be convex. - Any support for that assumption? - And "idea 1" still remains to be evaluated by my side. (quickfur here already gave some Input with respect to some dihedral angle restrictions. But so far I had no sparetime to look more closely into these...)
Which one would be convex again? I only remember two convex findings from your ideas, one was the same as an n,12-duoprism, and the other was the same as x4o3o3x. Did I miss another possible convex figure in there?
Yes, idea 3 was that n,12-douprism, and thus disproven to be of interest here.
But within idea 2 I had that thingy:
- Code: Select all
x4x x4x
x4x x4o x4o x4x
x4x x4o x4o x4x
x4x x4x
which had the inverse usage of octagons / squares within the lace city as sidpith has!
Here is the corresponding incidence matrix as well:
- Code: Select all
64 * | 1 1 1 1 1 0 0 | 1 1 1 1 1 1 1 1 1 0 0 | 1 1 1 1 1 1 0
* 16 | 0 0 0 0 4 2 2 | 0 0 0 0 0 4 4 2 2 4 1 | 0 0 4 2 2 1 2
------+----------------------+--------------------------------+------------------
2 0 | 32 * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 | 1 1 1 1 0 0 0 {8}-sides parallel to pseudo {4}
2 0 | * 32 * * * * * | 1 0 0 1 1 0 0 1 0 0 0 | 1 1 0 0 1 1 0 {8}-sides rel. dual to pseudo {4}
2 0 | * * 32 * * * * | 0 1 0 1 0 0 1 0 0 0 0 | 1 0 1 0 1 0 0 extension-para. op lacings
2 0 | * * * 32 * * * | 0 0 1 0 1 0 0 0 1 0 0 | 0 1 0 1 0 1 0 former op lacings
1 1 | * * * * 64 * * | 0 0 0 0 0 1 1 1 1 0 0 | 0 0 1 1 1 1 0
0 2 | * * * * * 16 * | 0 0 0 0 0 2 0 0 0 2 0 | 0 0 2 1 0 0 1 pseudo {4}-sides
0 2 | * * * * * * 16 | 0 0 0 0 0 0 2 0 0 2 1 | 0 0 2 0 1 0 2 extension edges
------+----------------------+--------------------------------+------------------
8 0 | 4 4 0 0 0 0 0 | 8 * * * * * * * * * * | 1 1 0 0 0 0 0
4 0 | 2 0 2 0 0 0 0 | * 16 * * * * * * * * * | 1 0 1 0 0 0 0 adj. cubes
4 0 | 2 0 0 2 0 0 0 | * * 16 * * * * * * * * | 0 1 0 1 0 0 0 between former op and trips
4 0 | 0 2 2 0 0 0 0 | * * * 16 * * * * * * * | 1 0 0 0 1 0 0 between ext. op and trip
4 0 | 0 2 0 2 0 0 0 | * * * * 16 * * * * * * | 0 1 0 0 0 1 0 adj. squippies
2 2 | 1 0 0 0 2 1 0 | * * * * * 32 * * * * * | 0 0 1 1 0 0 0
2 2 | 0 0 1 0 2 0 1 | * * * * * * 32 * * * * | 0 0 1 0 1 0 0
2 1 | 0 1 0 0 2 0 0 | * * * * * * * 32 * * * | 0 0 0 0 1 1 0
2 1 | 0 0 0 1 2 0 0 | * * * * * * * * 32 * * | 0 0 0 1 0 1 0
0 4 | 0 0 0 0 0 2 2 | * * * * * * * * * 16 * | 0 0 1 0 0 0 1
0 4 | 0 0 0 0 0 0 4 | * * * * * * * * * * 4 | 0 0 0 0 0 0 2
------+----------------------+--------------------------------+------------------
16 0 | 8 8 8 0 0 0 0 | 2 4 0 4 0 0 0 0 0 0 0 | 4 * * * * * * extension-para. op
16 0 | 8 8 0 8 0 0 0 | 2 0 4 0 4 0 0 0 0 0 0 | * 4 * * * * * former op
4 4 | 2 0 2 0 4 2 2 | 0 1 0 0 0 2 2 0 0 1 0 | * * 16 * * * * lacing cube
4 2 | 2 0 0 2 4 1 0 | 0 0 1 0 0 2 0 0 2 0 0 | * * * 16 * * * former op adj. trip
4 2 | 0 2 2 0 4 0 1 | 0 0 0 1 0 0 2 2 0 0 0 | * * * * 16 * * ext. op adj. trip
4 1 | 0 2 0 2 4 0 0 | 0 0 0 0 1 0 0 2 2 0 0 | * * * * * 16 * squippies
0 8 | 0 0 0 0 0 4 8 | 0 0 0 0 0 0 0 0 0 4 2 | * * * * * * 4 cube
So any support on the convexity of that fellow?
--- rk