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Francis Kurkdjian was born in Paris, France on 14 May 1969 to Armenian parents. [2] [3] [4] Having been exposed to music and dancing at a young age, Francis Kurkdjian wanted to be a ballet dancer during his youth.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations) "Chapter 10: Regular honeycombs in hyperbolic space".
It is constructed by congruent right triangles with 4, 8, and 10 triangles meeting at each vertex. The name 4-5 kisrhombille is by Conway, seeing it as a 4-5 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles. The image shows a Poincaré disk model projection of the hyperbolic plane.
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Circle Limit III is a woodcut made in 1959 by Dutch artist M. C. Escher, in which "strings of fish shoot up like rockets from infinitely far away" and then "fall back again whence they came".
Each triangle in this dual tiling, order 3-7 kisrhombille, represent a fundamental domain of the Wythoff construction for the symmetry group [7,3]. The dual tiling is called an order-3 bisected heptagonal tiling , made as a complete bisection of the heptagonal tiling , here shown with triangles with alternating colors.
A half symmetry [1+,4,5] = [5,5] coloring can be constructed with two colors of decagons. This coloring is called a truncated pentapentagonal tiling . Symmetry
In Coxeter notation can be represented as [8 *,4], removing two of three mirrors (passing through the octagon center) in the [8,4] symmetry. Adding a bisecting mirror through 2 vertices of an octagonal fundamental domain defines a trapezohedral *4422 symmetry .
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