An octagon is a polygon with 8 sides and 8 interior angles. The word 'Octagon' is derived from the Greek word, 'oktágōnon' which means eight angles. That is the reason why it is called an octagon.
What polygon has 8 sides Besides an octagon?
By definition, a polygon is a generic terms given to a 2-dimension image having 3 or more sides and 3 or more angles between the two adjoining sides. An octagon has 8 sides and 8 angles. Hence, by default it is considered as a polygon. Click to see full answer.
Is an obtuse triangle a polygon?
By definition, a polygon is a generic terms given to a 2-dimension image having 3 or more sides and 3 or more angles between the two adjoining sides. An octagon has 8 sides and 8 angles. Hence, by default it is considered as a polygon.
Is octagon irregular or regular polygon?
Octagon. An octagon is an 8-sided polygon (a flat shape with straight sides). First, have a play with an octagon: Regular or Irregular. When all angles are equal and all sides are equal it is regular, otherwise it is irregular
Does an octagon have an obtuse angle?
Octagon. In geometry, Octagon is a polygon that has 8 sides and 8 angles. That means the number of vertices and edges of an octagon is 8, respectively. In simple words, the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length.
Why is it called a polygon?
What is a polygon and why?
What are the properties of a octagon?
What is the difference between a polygon and octagon?
is that polygon is (geometry) a plane figure bounded by straight edges while octagon is (geometry) a polygon with eight sides and eight angles.
How do you identify a polygon?
What must a polygon have?
Is an octagon A polygon?
Is octagon a regular polygon?
What is a polygon in geometry?
How many sides does a polygon have?
What is the difference between a pentagon and a polygon?
is that polygon is (geometry) a plane figure bounded by straight edges while pentagon is (geometry) a polygon with five sides and five angles.
Does an octagon have 8 equal sides?
What is an octagon?
Convex, cyclic, equilateral, isogonal, isotoxal. In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square, t {4}, which alternates two types of edges.
How many sides does an octagon have?
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square, t {4}, which alternates two types of edges. A truncated octagon, t {8} is a hexadecagon, {16}.
What is the sum of all the internal angles of an octagon?
The diagonals of the green quadrilateral are equal in length and at right angles to each other. The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°.
What is the symbol for a regular octagon?
It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}.
What is a regular skew octagon?
The regular skew octagon is the Petrie polygon for these higher-dimensional regular and uniform polytopes, shown in these skew orthogonal projections of in A 7, B 4, and D 5 Coxeter planes .
Regular or Irregular
When all angles are equal and all sides are equal it is regular, otherwise it is irregular
Concave or Convex
A convex octagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
Is it an Octagon?
An octagon has 8 straight sides. The shape must also be closed (all the lines connect up):
Is an octagon a polygon?
Like the other polygon shapes, we have studied in geometry, such as triangle, square, pentagon, hexagon, rectangle, etc., the octagon is also a polygon. The points which define it different from other geometrical shapes is that it has 8 sides and 8 angles.
Is an octagon a regular octagon?
When an octagon has all equal sides and equal angles, then it is defined as a regular octagon. But if it has unequal sides and unequal angles, it is defined as an irregular octagon. See the figure below to see the difference between them.
How many sides does an octagon have?
Octagon is a polygon in geometry, which has 8 sides and 8 angles. That means the number of vertices is 8 and the number of edges is 8. All the sides are joined with each other end-to-end to form a shape. These sides are in a straight line form; they are not curved or disjoint with each other. Each interior angle of a regular octagon is 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°. In this article, let us discuss the octagon shape, its formulas, properties, and examples in detail.
Which octagon has all its angles pointing outside?
The octagon which has all its angles pointing outside or no angles are pointing inwards, is a convex octagon. The angles of the convex octagon are not more than 180°. And the octagon, which one of its angles pointing inward is a concave-shaped octagon.
What is the area of an octagon?
Area of the octagon is the region covered by the sides of the octagon. The formula for the area of a regular octagon which has 8 equal sides and all its interior angles are equal to 135°, is given by:
What is an octagon called when all the angles are pointing outwards?
If all the angles of an octagon are pointing outwards and the interior angles are not more than 180 degrees, then it is called convex polygon. If anyone of the angles pointing inwards, then it is called a concave polygon.
What is the sum of the interior angles of an octagon?
The total sum of the interior angles is 1080°, where each angle is equal to 135° (135×8 = 1080) Sum of all the exterior angles of the octagon is 360°, and each angle is 45° (45×8=360).
What is the meaning of the octagon?
Fun Facts about octagon. The word ‘Octagon’ has been derived from the Greek word ‘ὀκτάγωνον’ (oktágōnon) which means eight angles. This is how the shape with eight angles was named Octagon. During the 1850s and 1900s, many people started building their homes in the shape of an octagon as it is a symbol that represents rebirth, infinity, ...
How many angles does an octagon have?
An octagon has 8 exterior angles. The sum of the exterior angles of an octagon is 360°. Regular octagon: An octagon in which all sides and angles are equal. Each angle of a regular octagon is 135°. Irregular octagon: An octagon in which all sides and all angles are not equal.
What Are Octagons?
Chances are, you saw an octagon or two today, and you may not have even known it! Octagons are everywhere, and they have some pretty interesting features.
Octagons All Around!
Octagons are all around you! They may be tiny like those in a floor tile pattern, or very big, like the octagon ceiling in this image.
Regular vs Irregular Octagons
Regular octagons are easily recognized - they'll always have eight equal sides and eight equal angles. They are the typical shape you think of when you hear the word octagon. This is the type of shape we often see in signs, ceiling or floor tiles, or pieces of art.
Regular or Irregular
A regular polygon has all angles equal and all sides equal, otherwise it is irregular
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex.
Overview
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges. A truncated octagon, t{8} is a hexadecagon, {16}. A 3D analog of the octagon ca…
Properties of the general octagon
The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°.
If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal(that is…
Regular octagon
A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° ( radians). The central angle is 45° ( radians).
Skew octagon
A skew octagon is a skew polygon with 8 vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A skew zig-zag octagon has vertices alternating between two parallel planes.
A regular skew octagon is vertex-transitivewith equal edge lengths. In 3-dimensions it will be a zig-zag skew octagon and can be seen in the vertices a…
Symmetry of octagon
The regular octagon has Dih8 symmetry, order 16. There are 3 dihedral subgroups: Dih4, Dih2, and Dih1, and 4 cyclic subgroups: Z8, Z4, Z2, and Z1, the last implying no symmetry.
On the regular octagon, there are 11 distinct symmetries. John Conway labels full symmetry as r16. The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars) Cyclic symmetries in the middle column are labeled a…
Uses of octagons
The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa, Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery, Z…
See also
• Bumper pool
• Octagon house
• Octagonal number
• Octagram
• Octahedron, 3D shape with eight faces.
External links
• Octagon Calculator
• Definition and properties of an octagon With interactive animation