Polycairo

Author

Eric W. Weisstein
April 24, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/RecreationalMath/Polycairo.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Polycairo.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Tessellation

Graphics[{EdgeForm[Thin], White,Polygon[polyform[[10,5]][#]]&/@Tuples[Range[1,8],{3}]}]

Graphic for 2-sided

Column[Table[With[{form=10, order=ord, size=14, restrict=2, partition=6},Grid[Partition[Table[With[{sizer = N[size (.5 +Max[#]-Min[#])&/@Transpose[Flatten[polyform[[form,5]][#]&/@polyform[[form,4,restrict,order,n]],2]]]},Graphics[{EdgeForm[Thick],Red,Polygon[polyform[[form,5]][#]]& /@polyform[[form,4,restrict,order,n]]},ImageSize->sizer ]] ,
{n,1,Length[polyform[[form,4,restrict,order]]]}],partition,partition,1," "]]],{ord,1,4}]]

Sloane

<<Utilities`EISFormat`

Counts for 2-sided form, Sloane

{polyform[[10,2,2]], polyform[[10,7,2]]}

FindSequenceFunction[{1,2,5,17,55,206,781,3099,12421,50725}]

FormatSequence[{1,2,5,17,55,206,781,3099,12421,50725},
159866,1,
SequenceName->"Number of 2-sided n-polycairos.",
html["Polycairo"]
]