Sevenstar
From the first moment, this little picture shines on my home-page. This pattern stems from one of my first geometric constructions. Sevenfold symmetries, drawn accurately on large sheets of paper.

Here are some copies (click on a picture to see a larger version).
 The pattern above looks like this: the Sevenstar.

 Here is the construction of the Sevenstar, step by step, in the same way I do my crop circle reconstructions. 1. Draw a circle. Draw the horizontal and vertical centerlines. 2. Construct the inscribed heptagon (regular seven-sided polygon) of circle 1, pointing down.Notice, that a regular seven-sided polygon can not exactly be constructed using the ruler-and-compass method. (See also my remarks on the crop circle reconstruction pages). 3. Draw the seven "outer" diagonals of heptagon 2.(A regular seven-sided polygon has two sets of diagonals, "outer" diagonals, from any angular point to every second angular point, and "inner" diagonals, with two angular points in between). 4. Draw the seven "inner" diagonals of the heptagon enclosed by diagonals 3. 5. Construct the heptagon enclosed by diagonals 4.This is the basis for the central seven-sided polygon of the Sevenstar. 6. Draw the "outer" diagonals of the same heptagon as diagonals 4.The seven peripheral seven-sided polygons of the Sevenstar lie in the corners of this line pattern. 7. Draw the seven "inner" diagonals of heptagon 2. 8. Copy heptagon 5 seven times, and mirror each of them with respect to one of diagonals 7.(In fact, each heptagon should be constructed fully, but that's a step too far here! See the first of the six patterns at the top of this page for a hint). 9. Draw the shown connecting line between intersections of diagonals 3 and 7. Repeat this six times, for the corresponding symmetrical points. 10. Draw the shown connecting line between (other) intersections of diagonals 3 and 7. Repeat this six times, for the corresponding symmetrical points. 11. Remove all redundant parts from lines 9 and 10, such that this pattern remains. 12. Draw the seven "inner" diagonals of the heptagon enclosed by pattern 11 (lines 10). 13. Draw the seven "inner" diagonals of the heptagon enclosed by diagonals 12, and extend these up to the outermost lines (diagonals) 3. See also detail. 14. Draw the shown connecting line between intersections of diagonals 3 and lines 13. Repeat this six times, for the corresponding symmetrical points. 15. Remove all redundant parts from lines 3, 12, 13 and 14, such that this pattern remains. 16. Construct a circle tangent to heptagon 5 and lines 15, as shown. 17. Copy circle 16 seven times, to the angular points of heptagon 5. 18. Construct seven pairs of lines, two by two parallel to the sides of heptagon 5, tangent to circles 17. Make these lines join by extending or trimming, as shown. 19. Copy circle 16 seven times seven times, to the angular points of heptagons 8. 20. Repeat step 18 for all heptagons 8. 21. Copy circle 16 seven times two times, to the angular points of line pattern 11. 22. Repeat step 18 for all lines of pattern 11. 23. Copy circle 16 to all angular points of line pattern 15, 49 in total. 24. Repeat step 18 for all lines of pattern 15. 25. Lines 18, 20, 22 and 24 together make up all the constituent parts of the final pattern. 26. Remove all redundant parts, such that this interweaving pattern appears: the Sevenstar.