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YCor
YCor
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Among all convex pentagons, does the regular pentagon give least packing density?

Further question: For each n > 6$n > 6$, is the regular n$n$-gon the minimum of packing density?

An analogous question can be asked on covering -– for which values of n = 5$n= 5$ and above 6$6$, the regular n-gon gives the maximum covering density among all convex n$n$-gons (ie. is the least economical for covering)?

Do the answers to these questions depend on central symmetry -– whether n$n$ is odd or even?

Among all convex pentagons, does the regular pentagon give least packing density?

Further question: For each n > 6, is the regular n-gon the minimum of packing density?

An analogous question can be asked on covering - for which values of n = 5 and above 6, the regular n-gon gives the maximum covering density among all convex n-gons (ie. is the least economical for covering)?

Do the answers to these questions depend on central symmetry - whether n is odd or even?

Among all convex pentagons, does the regular pentagon give least packing density?

Further question: For each $n > 6$, is the regular $n$-gon the minimum of packing density?

An analogous question can be asked on covering – for which values of $n= 5$ and above $6$, the regular n-gon gives the maximum covering density among all convex $n$-gons (ie. is the least economical for covering)?

Do the answers to these questions depend on central symmetry – whether $n$ is odd or even?

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Nandakumar R
Nandakumar R
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Which convex pentagon gives least packing density?

Among all convex pentagons, does the regular pentagon give least packing density?

Further question: For each n > 6, is the regular n-gon the minimum of packing density?

An analogous question can be asked on covering - for which values of n = 5 and above 6, the regular n-gon gives the maximum covering density among all convex n-gons (ie. is the least economical for covering)?

Do the answers to these questions depend on central symmetry - whether n is odd or even?