# Mirror symmetric pentagon

(Redirected from Floret pentagon)
Mirror symmetric pentagon
Rank2
Elements
Edges2 + 2 + 1
Vertices2 + 2 + 1
Dyad, length ${\displaystyle {\sqrt {7}}}$
Dyad, length ${\displaystyle {\sqrt {3}}}$
Measures (edge lengths 1,2)
Area${\displaystyle {\frac {7{\sqrt {3}}}{4}}}$
Angles120° = ${\displaystyle 2\pi /3}$ radians
60° = ${\displaystyle \pi /3}$ radians
Central density1
Abstract & topological properties
Flag count10
Euler characteristic0
SurfaceCircle
OrientableYes
Properties
Flag orbits5
ConvexYes
Net count3
NatureTame

The mirror symetric 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:

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

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