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⁾

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⁾

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⁾