A **magic polygon** is a polygonal magic graph with integers on its vertices.

A **magic polygon** also called a **perimeter magic polygon**^{ [1] }^{ [2] } is a polygon with an integers on its sides that all add up to a magic sum.^{ [3] }^{ [4] } It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant, or magic sum.^{ [1] } Magic polygons are the generalization of other magic shapes^{ [5] } such as magic triangles.^{ [6] }

Victoria Jakicic and Rachelle Bouchat defined the magic polygon as an n-sidef regular polygons with 2n+1 nodes that the sum of the three nodes are equal. In their definition, 3×3 magic square can be viewed as a magic 4-gon. There are no magic odd-gon in this definition.^{ [7] }

Danielle Dias Augustoa and Josimar da Silva defined the magic polygon P(n,k) as a set of vertices of concentric n-gon and a center point. In this definition, Magic polygons of Victoria Jakicic and Rachelle Bouchat can be viewed as P(n,2) magic polygons. They also defined degenerated magic polygons^{ [8] }

In elementary geometry, a **polytope** is a geometric object with "flat" sides. It is a generalization in any number of dimensions of the three-dimensional polyhedron. Polytopes may exist in any general number of dimensions *n* as an *n*-dimensional polytope or ** n-polytope**. Flat sides mean that the sides of a (

In geometry, a **polygon** is a plane figure that is described by a finite number of straight line segments connected to form a closed *polygonal chain*. The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

In geometry, a **star polygon** is a type of non-convex polygon. **Regular star polygons** have been studied in depth; while star polygons in general appear not to have been formally defined, however certain notable ones can arise through truncation operations on regular simple and star polygons.

In Euclidean geometry, a **regular polygon** is a polygon that is equiangular and equilateral. Regular polygons may be either **convex** or **star**. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon, if the edge length is fixed.

In geometry, a **diagonal** is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word *diagonal* derives from the ancient Greek διαγώνιος *diagonios*, "from angle to angle" ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and later adopted into Latin as *diagonus*.

In geometry, a **dodecagon** or 12-gon is any twelve-sided polygon.

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an **interior****angle** if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.

In mathematics, **incidence geometry** is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles, continuity, betweenness, and incidence. An *incidence structure* is what is obtained when all other concepts are removed and all that remains is the data about which points lie on which lines. Even with this severe limitation, theorems can be proved and interesting facts emerge concerning this structure. Such fundamental results remain valid when additional concepts are added to form a richer geometry. It sometimes happens that authors blur the distinction between a study and the objects of that study, so it is not surprising to find that some authors refer to incidence structures as incidence geometries.

**Elementary mathematics** consists of mathematics topics frequently taught at the primary or secondary school levels.

In Euclidean geometry, an **equiangular polygon** is a polygon whose vertex angles are equal. If the lengths of the sides are also equal then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths.

In graph theory, a **Moore graph** is a regular graph of degree *d* and diameter *k* whose number of vertices equals the upper bound

In geometry, a **257-gon** is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 45,900°.

In geometry, a **Coxeter–Dynkin diagram** is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors. It describes a kaleidoscopic construction: each graph "node" represents a mirror and the label attached to a branch encodes the dihedral angle order between two mirrors, that is, the amount by which the angle between the reflective planes can be multiplied by to get 180 degrees. An unlabeled branch implicitly represents order-3.

In geometry, a **skew polygon** is a polygon whose vertices are not all coplanar. Skew polygons must have at least four vertices. The *interior* surface of such a polygon is not uniquely defined.

In geometry, a **Robbins pentagon** is a cyclic pentagon whose side lengths and area are all rational numbers.

In geometry, a **domino tiling** of a region in the Euclidean plane is a tessellation of the region by dominos, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they correspond to adjacent squares.

In mathematics, an **associahedron***K*_{n} is an (*n* − 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a word of *n* letters and the edges correspond to single application of the associativity rule. Equivalently, the vertices of an associahedron correspond to the triangulations of a regular polygon with *n* + 1 sides and the edges correspond to edge flips in which a single diagonal is removed from a triangulation and replaced by a different diagonal. Associahedra are also called **Stasheff polytopes** after the work of Jim Stasheff, who rediscovered them in the early 1960s after earlier work on them by Dov Tamari.

In mathematics, the **pentagram map** is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper though it seems that the special case, in which the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch and a 1945 paper of Theodore Motzkin. The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism. It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning the diagonals of a polygon.

In combinatorics, the **Schröder–Hipparchus numbers** form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin

- 1 2 "Perimeter Maghic Polygons".
*www.trottermath.net*. Archived from the original on 2018-01-12. Retrieved 2017-02-12. - ↑ "Perimeter Magic Polygon >k=3".
*www.magic-squares.net*. Retrieved 2017-02-12. - ↑ Staszkow, Ronald (2003-05-01).
*Math Skills: Arithmetic with Introductory Algebra and Geometry*. Kendall Hunt. p. 199. ISBN 9780787292966.Magic polygon math.

- ↑ Bolt, Brian (1987-04-09).
*Even More Mathematical Activities*. Cambridge University Press. ISBN 9780521339940. - ↑ Croft, Hallard T.; Falconer, Kenneth; Guy, Richard K. (2012-12-06).
*Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics*. Springer Science & Business Media. ISBN 9781461209638. - ↑ Heinz, Harvey D. "Perimeter Magic Triagonals".
*recmath.org*. Retrieved 2017-02-12. - ↑ Jakicic, Victoria; Bouchat, Rachelle (2018). "Magic Polygons and Their Properties". arXiv: 1801.02262 [math.CO].
- ↑ Danniel Dias Augusto; Josimar da Silva Rocha (2019). "Magic Polygons and Degenerated Magic Polygons: Characterization and Properties". arXiv: 1906.11342 [math.CO].

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