Floret pentagon

Floret pentagon
Rank	2
Elements
Edges	2 + 2 + 1
Vertices	2 + 2 + 1
Vertex figures	Dyad, length 2
	Dyad, length ${\sqrt {7}}$
	Dyad, length ${\sqrt {3}}$
Measures (edge lengths 1,2)
Area	${\frac {7{\sqrt {3}}}{4}}$
Angles	120° = $2\pi /3$ radians
	60° = $\pi /3$ radians
Central density	1
Abstract & topological properties
Flag count	10
Euler characteristic	0
Surface	Circle
Orientable	Yes
Properties
Convex	Yes
Net count	3
Nature	Tame

The floret pentagon is a type of irregular pentagon with mirror symmetry but no rotational symmetry. It appears as in the vertex figures of several snub polyhedra and thus as faces of their duals.

Vertex coordinates

Coordinates for a floret pentagon with minor edge length 1 and major edge length 2 are:

• $\left(\pm 1,\,0\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{2}}\right)$,
• $\left(0,\,{\sqrt {3}}\right)$.

These coordinates lie coincide with vertices of a triangular tiling, and the floret pentagon can be dissected into 7 equilateral triangles.