Butterfly

Butterfly
(OFF file)
Rank	2
Space	Spherical
Notation
Bowers style acronym	Butter
Elements
Edges	2+2
Vertices	2+2
Vertex figure	Dyad
Related polytopes
Army	Traz
Dual	Butterfly
Conjugate	Butterfly
Topological properties
Orientable	No
Properties
Symmetry	A1×I, order 2
Convex	No
Nature	Tame

A butterfly or butter, also called an antiparallelogram, is a non-convex quadrilateral with the vertices of an isosceles trapezoid. It uses the two lateral sides of the trapezoid, along with the other two sides being crossing diagonals.

In vertex figures

Butterflies in vertex figures

Name	Picture	Edge lengths
Small rhombihexahedron		√2, √2+√2
Great rhombihexahedron		√2, √2–√2
Rhombicosahedron		√2, √3
Small rhombidodecahedron		√2, √(5+√5)/2
Great rhombidodecahedron		√2, √(5–√5)/2
Small dodecicosahedron		√3, √(5+√5)/2
Great dodecicosahedron		√3, √(5–√5)/2