temarimath.info

Notebook Entry - 060507

Finished Views

Without gold pentagon outlines  
With the gold pentagon outlines  

Source

None, my own interpretation based on Conway quintomino solution from Glenna

Classification

C10, starburst

Size

23cm circumference

Materials

Wrap

cream cone thread

Marking

Very fine gold

Design threads

#5 perle cotton purple (DMC209), yellow (DMC727), green (Anchor261), orange (DMC922), blue (Anchor145)

Gold Rush 18 gold color

Division/Marking

C10

Directions

See Glenna's notes about marking the colors for a Conway quintomino solution. For each triangle of the pentagon work pine needle stitches radiating from the center of the pentagon (6 lines) to just before the edge of the pentagon. Use the correct color. You will end up with 5 different colored sections in each pentagon. Outline the pentagons with one row of gold. Adjust the stitching path so there is only one row of gold between each pair of pentagons.

Notes

This was done in response to Glenna's email about a temari interpretation of John H. Conway's solution to a quintomino problem. Quintominos are pentagons split into triangles and colored with 5 colors. There are 12 possibilities of color sequences without allowing duplicates based on rotation or reflection symmetry. The problem is to take the 12 quintominoes and place them together in a dodecahedron (or on a sphere) so that each side touches another side of the same color. There are three solutions. I think it would be neat to have a set of all three solutions. Glenna's version of Conway quintomino solutionGlenna interpreted the temari differently, with an open pentagon and each side stitched with a different color. The pentagons are smaller leaving blank space to highlight the pentagon shape. I think it is neat that we both came up with very different interpretations of the same math problem.

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