# Kiyoko Urata

Kiyoko Urata (1926-), a Temari artist was the president of
Naniwa-Temari society in Osaka, Japan. The Temaris with icosahedral
symmetry shown here were embroidered by her. Having no mathematical
background, she made these icosahedral patterns by trial and error.
Her original technique are compiled in her book “Naniwa Temaris”
(1995).

Any spherical object was usually called Mari in ancient Japan. Temari
is a ball held in hands (‘Te’). It has a spherical core made of cloth,
chaff or wood in the past, or polystyrene in present times. On the
surface, various spherical polyhedral patterns are subsequently
embroidered by means of more colorful strings.

Statement and Description by Koji Miyazaki

From around the 18th century, making Temari was enjoyed as a popular pastime among ladies. They seem to be usually decorated with dihedral, tetrahedral, or octahedral symmetry, because icosahedral symmetry was not common in Japan then. Around 1950, a high school teacher of mathematics taught a Temari artist how to decide the position of vertices of a spherical regular icosahedrons to use one of the sphere's poles as one of the icosahedron's vertices first, then to wind a string along a great circle through the pole and to plot a point on the great circle from the pole whose distance is G/6+G/100, where G is the length of the great circle to be the second vertex of the icosahedron. This is how icosahedral Temari was started.