Talk:Moser spindle

The very first paragraph contains the statement: "It is a unit distance graph" In addition, the first paragrapgh under construction states: "As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute-angled vertices are a unit distance apart from each other.

The first paragraph under the "Other properties and applications" states: "The Moser spindle is a planar graph, meaning that it can be drawn without crossings in the plane. However, it is not possible to form such a drawing with straight line edges that is also a unit distance drawing;"

There is the contradiction.

Also, the first picture of the Moser spindle connects the non-sharing vertices with an edge that is greater than a unit length and is decidedly different than the picture below it which has a Moser spindle containing edges that are all of unit length. — Preceding unsigned comment added by 71.178.35.32 (talk) 21:36, 25 May 2018 (UTC)

There is no contradiction. Unit distance graphs may have crossings. This one can be drawn as a unit distance graph (with crossings) or as a planar graph (without crossings, but with the edges not all having unit length). The two drawings are different, but they are drawings of the same graph. —David Eppstein (talk) 23:20, 25 May 2018 (UTC)