Calculations at a regular octagram. This is constructed by the medium diagonals of a regular octagon. It contains within itself a Star of Lakshmi with the edge length of the squares a.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
Lengths, diagonal, chord and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The octagram consists of the eight intermediate diagonals of a regular octagon, those are the diagonals with two vertices between. Hereby, every third vertex is connected to another. The octagram is unicursal. This means, the edges belong to a single closed circuit, much like the pentagram and the unicursal hexagram.
If the major diagonals of a regular octagon are seen as a distinct form, this consists solely of eight straight lines that are arranged symmetrically and intersect at a single point. This form possesses no interior area, it is a one-dimensional star. Conversely, the minor diagonals of a regular octagon yield another two-dimensional star, the Star of Lakshmi.
The octagram is used for symbolic and decorative purposes, where the orientation, whether one or two points face upward, plays a significant role. In terms of its geometric properties, however, this distinction is entirely irrelevant. When two points face upward, as shown in the accompanying graphic, the shape appears more rectilinear, as it features both horizontal and vertical lines. With a single point facing upward, it more closely resembles the conventional image of a star.
This octagram is axially symmetric with respect to eight axes. Four of those passing through pairs of opposite convex vertices, and another four passing through pairs of opposite notches or inward-pointing vertices. It is centrally symmetric with respect to the intersection point of all these axes of symmetry, which also is the center of the octagram. Furthermore, it possesses rotational symmetry about this point for rotations of 45 degrees and its multiples.