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An icosahedron has 20 faces in the shape of congruent equilateral triangles, 30 edges, 12 vertices and 15 planes of symmetry. By shearing the vertices of the icosahedron, we obtain a semi-formal polyhedron called the truncated icosahedron. 1)

Everywhere is north

Which direction can we not look while standing at the South Pole? Neither east, nor west, nor south. At the South Pole, every direction is north. 2)

Möbius strip

A Möbius strip has only one side and only one edge. Traveling along the edge of the ribbon, we will arrive at a location corresponding to the starting point, but “on the other side”. Continuing to travel further, we will arrive at the starting point again. 3)


A clock's hour hand makes two revolutions per day, while the minute hand makes 24 revolutions — so it passes the hour hand 22 times. To put it another way, during each hour the hands pass each other once, except for 11:00-12:00 and 23:00-24:00 hours, when the minute hand “catches up” with the hour hand at the end of the hour. 4)


An ellipsoid is a surface whose planar sections are all ellipses. Sometimes this word is also used to describe a solid bounded by this surface. An example of an ellipsoid is a rugby ball. 5)

geometry.txt · Last modified: 2021/09/06 12:42 by rapidplatypus