







A geodesic dome 
20070925 

From Roger: In my ScienceFiction 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 
20010501 

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 
20000917 

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 
20000621 

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 nonpolygons 
19980224 

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. 

