Compound of two pentagons

From Polytope Wiki
(Redirected from Stellated decagon)
Jump to navigation Jump to search
Compound of two pentagons
Rank2
TypeRegular
Notation
Bowers style acronymSadeg
Schläfli symbol{10/2}
Elements
Components2 pentagons
Edges10
Vertices10
Vertex figureDyad, length (1+5)/2
Measures (edge length 1)
Circumradius
Inradius
Area
Angle108°
Central density2
Number of external pieces20
Level of complexity2
Related polytopes
ArmyDec, edge length
DualCompound of two pentagons
ConjugateCompound of two pentagrams
Convex coreDecagon
Abstract & topological properties
Flag count20
Euler characteristic2
OrientableYes
Properties
SymmetryI2(10), order 20
ConvexNo
NatureTame

The stellated decagon or sadeg is a polygon compound composed of two pentagons. As such it has 10 edges and 10 vertices.

As the name suggests, it is the first stellation of the decagon.

Its quotient prismatic equivalent is the pentagonal antiprism, which is three-dimensional.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a stellated decagon of edge length 1 centered at the origin are given by:

Variations[edit | edit source]

The stellated decagon can be varied by changing the angle between the two component pentagons from the usual 36°. These 2-pentagon compounds generally have a dipentagon as their convex hull and remain uniform,but not regular, with pentagonal symmetry only.

External links[edit | edit source]


\pm