







A geodesic dome 
20070925 

Roger pose la question : 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. Chris Fisher lui répond. 





Tiling a floor 
20010501 

Sarah pose la question : 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? Claude Tardif lui répond. 





Tessellations 
20000917 

Lindsay pose la question : 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? Chris Fisher lui répond. 





Cairo tesselation and Archimedean duals 
20000621 

Joyce DuVall pose la question : 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? Penny Nom lui répond. 





Tessellations of nonpolygons 
19980224 

Ellen Goldwasser pose la question : 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! Penny Nom lui répond. 

