Schläfli symbol {10/3}t{5/3} Internal angle (degrees) 72° | Edges and vertices 10 Symmetry group Dihedral (D10) Dual polygon self | |
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In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.
Contents
The name decagram combine a numeral prefix, deca-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆς (grammēs) meaning a line.
Regular decagram
For a regular decagram with unit edge lengths, the proportions of the crossing points on each edge are as shown below.
Applications
Decagrams have been used as one of the decorative motifs in girih tiles.
Related figures
A regular decagram is a 10-sided polygram, represented by symbol {10/n}, containing the same vertices as regular decagon. Only one of these polygrams, {10/3} (connecting every third point), forms a regular star polygon, but there are also three ten-vertex polygrams which can be interpreted as regular compounds:
Deeper truncations of the regular pentagon and pentagram can produce intermediate star polygon forms with ten equally spaced vertices and two edge lengths that remain vertex-transitive (any two vertices can be transformed into each other by a symmetry of the figure).