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A geodesic dome 2007-09-25
From Roger:
In my Science-Fiction series, I have a Dyson's Sphere tiled with regular hexagons. The number of hexagons is over 300,000 and the radius of the Sphere is roughly 80,000,000 miles. The actual size of the Sphere and hexagons have been left flexible until I can come up with a definite number of hexagons that would fit. My problem is the pattern of hexagons which would fit within the sphere without leaving gaps or overlapping.

My best guess has been to use four equilateral triangles composed of 78606 hexagons, (396 per edge) arranged around the sphere with six 'zippers' to connect them and four 'caps' at the points, for a total of 316804 hexagons. Given the fact that each Hex is the same size, does this seem plausible? Is there some pattern formula I can use to play with these figures? Simple divsion of areas will not work if the number derived will not fit into the pattern to leave a perfectly tiled surface. Thank you.

Answered by Chris Fisher.
Tiling a floor 2001-05-01
From Sarah:
Cut out of paper or cardboard a quadrilateral having no two sides parallel, no two sides of equal length and no indentations. Can an endless floor be tiled with copies of such a figure?
Answered by Claude Tardif.
Tessellations 2000-09-17
From Lindsay:
What is the word that means a shape repeated over and over again to make something like a quilt pattern?

Note: I'm pretty sure it is either a fractal or tesselation. Could it be that the pattern itself is a fractal but the entire quilt would be a tesselation?

Answered by Chris Fisher.
Cairo tesselation and Archimedean duals 2000-06-21
From Joyce DuVall:
I am looking for a picture of the Cairo tesselation, and pictures of the Archimedean duals. Do you know of any good web sites or books?
Answered by Penny Nom.
Tessellations of non-polygons 1998-02-24
From Ellen Goldwasser:
Hi! My name is Ellen Goldwasser. I'm a seventh grade student and I'm doing a prodject on tessellation. My question is: why will certain shapes (not polygons) tessellate? Thanks for your help!
Answered by Penny Nom.



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