Unique Polypents with Star Symmetry and Minimum Perimeter
Introduction
A polypent is made by joining regular pentagons
edge to edge.
Some polypents have star symmetry.
This is the symmetry of a five-pointed star, 5-rotary with horizontal
reflection.
The number of cells in such a polypent must be a multiple of 5 or
one greater than a multiple of 5.
For some numbers of cells, there is a unique star-symmetric polypent
with minimum perimeter, including the perimeters of the holes.
Here I show such unique polypents for up to 50 cells.
See also Unique Polypents
with Full Symmetry and Minimum Perimeter.
Enumeration
Number
of Cells | Minimum
Perimeter | Number
of
Polypents |
|---|
| 1 | 5 | 1 |
| 5 | — | 0 |
| 6 | 20 | 1 |
| 10 | 30 | 2 |
| 11 | — | 0 |
| 15 | 45 | 2 |
| 16 | 50 | 1 |
| 20 | 60 | 6 |
| 21 | 55 | 1 |
| 25 | 75 | 9 |
| 26 | 70 | 2 |
| 30 | 80 | 1 |
| 31 | 85 | 3 |
| 35 | 95 | 5 |
| 36 | 90 | 2 |
| 40 | 100 | 1 |
| 41 | 105 | 3 |
| 45 | 115 | 1 |
| 46 | 120 | 6 |
| 50 | 130 | 7 |
Polypents
1 Cell, Perimeter 5
6 Cells, Perimeter 20
16 Cells, Perimeter 50
21 Cells, Perimeter 55
30 Cells, Perimeter 80
40 Cells, Perimeter 100
45 Cells, Perimeter 115
Last revised 2023-10-30.
Back to Polyform Catalogues
< Polyform Curiosities
Col. George Sicherman
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