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Obtuse triangle formed by the side and diagonals of a regular heptagon
regular heptagon. All heptagonal triangles are similar (have the same shape), and so they are collectively known as the heptagonal triangle. Its angles
Heptagonal_triangle
Shape with seven sides
regular heptagon. Apart from the heptagonal prism and heptagonal antiprism, no convex polyhedron made entirely out of regular polygons contains a heptagon as
Heptagon
Triangles without a right angle
acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle
Acute_and_obtuse_triangles
Curved triangle with constant width
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed
Reuleaux_triangle
Tiling of the hyperbolic plane
the heptagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {7,3}, having three regular heptagons around
Heptagonal_tiling
Shape with three equal sides
ISBN 978-1-61444-216-5. Bankoff, Leon; Garfunkel, Jack (January 1973). "The heptagonal triangle". Mathematics Magazine. 46 (1): 7–19. doi:10.1080/0025570X.1973.11976267
Equilateral_triangle
Relation between sides of a right triangle
{1}{q}}={\frac {1}{r}}} where the denominators are squares and also for a heptagonal triangle whose sides p, q, r are square numbers. One of the consequences of
Pythagorean_theorem
sides Triangle – 3 sides Acute triangle Equilateral triangle Heptagonal triangle Isosceles triangle Golden Triangle Obtuse triangle Rational triangle Heronian
List of two-dimensional geometric shapes
List_of_two-dimensional_geometric_shapes
Semiregular tiling of the hyperbolic plane
the reflection domains for the (2,3,n) triangle groups – for the heptagonal tiling, the important (2,3,7) triangle group. See also the uniform tilings of
3-7_kisrhombille
Polynomial equation of degree 3
In addition, the ratio of the inradius to the circumradius of a heptagonal triangle is one of the solutions of a cubic equation. The values of trigonometric
Cubic_equation
inequality Heilbronn triangle problem Heptagonal triangle Heronian triangle Heron's formula Hofstadter points Hyperbolic triangle (non-Euclidean geometry)
List_of_triangle_topics
Semiregular tiling of the hyperbolic plane
In geometry, the truncated heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one triangle and two tetradecagons on each vertex
Truncated_heptagonal_tiling
There are 14 edges where a triangle meets a heptagon, and an additional 14 edges where two triangles meet. The heptagonal antiprism was first illustrated
Heptagonal_antiprism
Figurate number
numbers or triangle numbers are the sequence of positive integers that can be represented as a lattice of points arranged in an equilateral triangle. The triangular
Triangular_number
number that is the sum of 9 positive 5th powers 1071 = heptagonal number 1072 = centered heptagonal number 1073 = number that is the sum of 12 positive 5th
1000_(number)
Natural number
number, a heptagonal number, and a Harshad number. 112 is the number of connected graphs on 6 unlabeled nodes. If an equilateral triangle has sides of
112_(number)
4-D shape
48. It has 24 triangle, 24 square and 4 hexagon faces. It has 60 edges, and 24 vertices. A heptagonal antiprismatic prism or heptagonal antiduoprism is
Uniform_antiprismatic_prism
isometries) with this triangle for fundamental domain; the associated tiling is the order-3 bisected heptagonal tiling. The (2,3,7) triangle group is defined
(2,3,7)_triangle_group
Natural number
equilateral triangles of varying sizes in it. The Metonic cycle is 235 synodic months. Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers)".
235_(number)
Semiregular tiling of the hyperbolic plane
called a heptakis heptagonal tiling, named for being constructible as a heptagonal tiling with every heptagon divided into seven triangles by the center point
Truncated order-7 triangular tiling
Truncated_order-7_triangular_tiling
Polyhedron with eight triangular faces
five triangular faces. Heptagonal pyramid: One face is a heptagon (usually regular), and the remaining seven faces are triangles (usually isosceles). It
Octahedron
Equation of the form 1/a + 1/b = 1/c
other inscribed square. The sides of a heptagonal triangle, which shares its vertices with a regular heptagon, satisfy the optic equation. For a lens
Optic_equation
Natural number
seven-sided shape is a heptagon. The regular n-gons for n ⩽ 6 can be constructed by compass and straightedge alone, which makes the heptagon the first regular
7
Concept in geometry
small cubicuboctahedron. The dual order-3 heptagonal tiling has the same symmetry group, and thus yields heptagonal tilings of Hurwitz surfaces. It is related
Order-7_triangular_tiling
Semiregular tiling of the hyperbolic plane
geometry, the order-3 snub heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are four triangles and one heptagon on each vertex. It has
Snub_triheptagonal_tiling
Natural number
integers 196 to 210 and sum of the integers 211 to 224 3046 – centered heptagonal number 3052 – decagonal number 3059 – centered cube number 3061 – prime
3000_(number)
Natural number
numbers. Only three such pairs of numbers are known. Rows in Pascal's triangle can be seen as representation of powers of 11. An 11-sided polygon is called
11_(number)
Symmetric subdivision in hyperbolic geometry
around each vertex. For example, 7.7.7 represents the heptagonal tiling which has 3 heptagons around each vertex. It is also regular since all the polygons
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
Coins by shape
coin is seven-sided. The British twenty pence and fifty pence coins are heptagonal Reuleaux polygons, as is the United Arab Emirates 50 fils coin, the Barbados
Coinage_shapes
Constant-width curve of equal-radius arcs
example, the Reuleaux triangle, which in turn is named after 19th-century German engineer Franz Reuleaux. The Reuleaux triangle can be constructed from
Reuleaux_polygon
Geometric tiling
the hyperbolic plane. At each vertex of the tiling there is one triangle and one heptagon, alternating between two squares. The tiling has Schläfli symbol
Rhombitriheptagonal_tiling
Star polygon with 7 sides
(grammē) meaning a line. In general, a heptagram is any self-intersecting heptagon (7-sided polygon). There are two regular heptagrams, labeled as {7/2} and
Heptagram
Compact Riemann surface of genus 3
a given fundamental triangle give a set of 3 generating reflections). This tiling is a quotient of the order-3 bisected heptagonal tiling of the hyperbolic
Klein_quartic
Generalization of Pythagorean theorem
theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides a {\displaystyle a} , b {\displaystyle
Law_of_cosines
Polyhedron with 14 faces
triangles, 2 squares, 4 pentagons) Tetradecahedra having at least one irregular face: Heptagonal bipyramid (14 triangles) (see Dipyramid) Heptagonal trapezohedron
Tetradecahedron
(n−1)-face Triangle Equilateral triangle Isosceles triangle Golden triangle (mathematics) Scalene triangle Right triangle Oblique triangle Acute triangle Obtuse
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Method of drawing geometric objects
general case; and in 39 the required triangle exists but is not constructible. Twelve key lengths of a triangle are the three side lengths, the three
Straightedge and compass construction
Straightedge_and_compass_construction
Regular polygon that can be constructed with compass and straightedge
pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with
Constructible_polygon
Triangular array of natural numbers
k\leq n} form a triangular array of natural numbers, called the Narayana triangle, that occur in various counting problems. They are named after Canadian
Narayana_number
Pentagram Regular polygon Equilateral triangle Simplex Square Cross-polytope Hypercube Pentagon Hexagon Heptagon Octagon Enneagon Decagon Hendecagon Dodecagon
List_of_mathematical_shapes
Natural number
code for "Payment Required". The area code for Nebraska. 403 = 13 × 31, heptagonal number, Mertens function returns 0. First number that is the product of
400_(number)
Polyhedron formed by joining mirroring pyramids base-to-base
all their edges are equal in length, these shapes consist of equilateral triangle faces, making them deltahedra; the triangular bipyramid and the pentagonal
Bipyramid
Recursive integer sequence
be cut into triangles by connecting vertices with non-crossing line segments (a form of polygon triangulation). The number of triangles formed is n and
Catalan_number
Semiregular tiling of the hyperbolic plane
are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling. Drawing the tiles colored as red on the original faces, yellow
Truncated triheptagonal tiling
Truncated_triheptagonal_tiling
Natural number
digits as its distinct prime factors 736 = 25 × 23. It is: a centered heptagonal number a happy number a Harshad number a nice Friedman number since 736
700_(number)
Natural number
836 = 22 × 11 × 19, weird number 837 = 33 × 31, the 36th generalized heptagonal number 838 = 2 × 419, palindromic number, number of distinct products
800_(number)
Polyhedron with 9 faces
faces around a regular octagonal base. Heptagonal prism: a prismatic uniform polyhedron with two regular heptagon faces and seven square faces. Elongated
Enneahedron
Semiregular tiling of the hyperbolic plane
hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli symbol
Triheptagonal_tiling
2007 American film
Curtis Luciani as King of Lineland Shannon McCormick as Triangle Guard T. Lynn Mikeska as Heptagon Mother Robert Murphy as Pentagon Reporter Garry Peters
Flatland (2007 Johnson and Travis film)
Flatland_(2007_Johnson_and_Travis_film)
Polyhedron made of congruent kites arranged radially
are not to be confused with deltahedra, whose faces are equilateral triangles. Twisted trigonal, tetragonal, and hexagonal trapezohedra (with six, eight
Trapezohedron
Numbers obtained by adding the two previous ones
89), ... . The middle side of each of these triangles is the sum of the three sides of the preceding triangle. The Fibonacci cube is an undirected graph
Fibonacci_sequence
Polygon with equally angled vertices
density q. Equiangular triangles must be convex and have 60° internal angles. It is an equilateral triangle and a regular triangle, ⟨3⟩={3}. The only degree
Equiangular_polygon
Area of a right triangle with rational-numbered sides
a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition includes all
Congruent_number
Centered figurate number that represents a triangle with a dot in the center
triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center
Centered_triangular_number
Concept in combinatorics
also gives the lazy caterer's sequence. The fourth column of Bernoulli's triangle (k = 3) gives the cake numbers for n cuts, where n ≥ 3. The sequence can
Cake_number
Form of an object
their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles
Shape
Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon
List_of_polygons
Automorphism group of the Klein quartic
curvature and then tiled with regular (hyperbolic) heptagons, as a quotient of the order-3 heptagonal tiling, with the symmetries of the surface as a Riemannian
PSL(2,7)
Count of the possible partitions of a set
be calculated by creating the so-called Bell triangle, also called Aitken's array or the Peirce triangle after Alexander Aitken and Charles Sanders Peirce
Bell_number
Tiling of the hyperbolic plane
triangles, 14 of which form each heptagram. Each point of the hyperbolic plane that does not lie on a heptagram edge belongs to the central heptagon of
Order-7_heptagrammic_tiling
Partition of a simple polygon into triangles
of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union
Polygon_triangulation
Tool for trisecting angles
in geometry to refer to a different shape, the arbelos (a curvilinear triangle bounded by three mutually tangent semicircles). The basic shape of a tomahawk
Tomahawk_(geometry)
Two raised to an integer power
triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star non-centered
Power_of_two
Fractal creation method
produce a fractal shape. Using a regular triangle and the factor 1/2 will result in the Sierpinski triangle, while creating the proper arrangement with
Chaos_game
Polyhedral number representing a tetrahedron
be found in the fourth position either from left or right in Pascal's triangle. This proof uses the fact that the nth triangular number is given by T
Tetrahedral_number
Sequence of integers
article must be adjusted with appropriate offsets. In the spiral, each triangle shares a side with two others giving a visual proof that the Padovan sequence
Padovan_sequence
Covering by shapes without overlaps or gaps
see Pentagonal tiling, for N = 6, see Hexagonal tiling, for N = 7, see Heptagonal tiling and for N = 8, see octagonal tiling. With non-convex polygons,
Tessellation
Plane figure bounded by line segments
vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. More
Polygon
sum-free sequence is less than 2.8570 . The sum of the reciprocals of the heptagonal numbers converges to a known value that is not only irrational but also
List_of_sums_of_reciprocals
Number in the 5th cell of any row of Pascal's triangle
triangulo-triangular number) is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from left to right or from
Pentatope_number
of God) Catholic iconography, Masonic symbolism The eye of God within a triangle, representing the Holy Trinity, and surrounded by holy light, representing
List_of_occult_symbols
Result of multiplying four instances of a number together
fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a fourth power cannot be written as the
Fourth_power
Number of paths between grid corners, allowing diagonal steps
arranged in a triangular array resembling Pascal's triangle, also called the tribonacci triangle, in which each number is the sum of the three numbers
Delannoy_number
Theorem in algebraic geometry
symmetry group is the full (2,3,7) triangle group generated by the reflections across the sides of a single fundamental triangle with the angles π/2, π/3 and
Hurwitz's automorphisms theorem
Hurwitz's_automorphisms_theorem
Natural number
four consecutive primes (151 + 157 + 163 + 167) a nontotient a centered heptagonal number 639 = 32 × 71. It is: the sum of the first twenty primes ISO 639
600_(number)
1/p + 1/q < 1/2 gives a hyperbolic tiling. In fact, for the general Schwarz triangle (p, q, r) the same holds true for 1/p + 1/q + 1/r < 1. There are a number
List_of_regular_polytopes
Paper model
2023. Retrieved October 26, 2012. McIntosh, Harold V. (March 11, 2000). "Heptagonal Flexagons". Cinvestav.mx. Universidad Autónoma de Puebla. Archived from
Flexagon
Product of an integer with itself
an integer power Pythagorean triple – Integer side lengths of a right triangle Quadratic residue – Integer that is a perfect square modulo some integer
Square_number
Polyhedron with parallel bases connected by triangles
images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented by the Conway notation An. Antiprisms are a subclass
Antiprism
Type of uniform 4-polytope in four-dimensional geography
and 4 hexagonal prisms - (same as 4-6 duoprism) Heptagonal prismatic prism - - 7 cubes and 4 heptagonal prisms - (same as 4-7 duoprism) Octagonal prismatic
Prismatic_uniform_4-polytope
Marked objects for finding random numbers
starting from 6 Bipyramids, the duals of the infinite set of prisms, with triangle faces: any multiple of 4 (so that a facet faces up), starting from 8 Disphenoids
Dice
Number of stacked spheres in a pyramid
only one acute triangle (itself), a regular pentagon has five acute golden triangles within it, a regular heptagon has 14 acute triangles of two shapes
Square_pyramidal_number
Polyhedron made by truncating one end of a trapezohedron
by a new face (diminishment). It has one regular n-gonal base face, n triangle faces around the base, and n kites meeting on top. The kites can also be
Diminished_trapezohedron
Number that represents a hexagon with a dot in the center
1–7–9–7–1 (repeating with period 5). This follows from the last digit of the triangle numbers (sequence A008954 in the OEIS) which repeat 0-1-3-1-0 when taken
Centered_hexagonal_number
Solid made from 2 rotunda joined base-to-base
a bicupola but instead of alternating squares and triangles, it alternates pentagons and triangles around an axis. There are two forms, ortho- and gyro-:
Birotunda
Rock castle in Merzalben, Germany
metres (200 ft) wide. Gräfenstein is the only castle in Germany with a heptagonal keep or bergfried. This may still be climbed today up a narrow spiral
Gräfenstein_Castle
Number divisible only by 1 and itself
two-dimensional grid so that no three are in a line, or so that every triangle formed by three of the points has large area. Another example is Eisenstein's
Prime_number
Polyhedron with two kinds of faces
7)2 - a quasiregular tiling based on the order-7 triangular tiling and heptagonal tiling. Coxeter, H.S.M. et al. (1954) also classify certain star polyhedra
Quasiregular_polyhedron
two regular heptagons and three equilateral triangles around every vertex. Drawn in chiral pairs, with edges missing between black triangles: A double symmetry
Snub_heptaheptagonal_tiling
Numbers parameterizing ways to partition a set
relation is specified by mapping n and k coordinates onto the Sierpiński triangle. More directly, let two sets contain positions of 1's in binary representations
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Cartesian product of two polytopes
example: a triangular-pentagonal duoprism is the Cartesian product of a triangle and a pentagon. An alternative, more concise way of specifying a particular
Duoprism
Count of permutations by cycles
for the Stirling numbers of the first kind, similar in form to Pascal's triangle. These values are easy to generate using the recurrence relation in the
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Pictorial representation of symmetry
Three mirrors in a triangle form images seen in a traditional kaleidoscope and can be represented by three nodes connected in a triangle. Repeating examples
Coxeter–Dynkin_diagram
Theorem relating the number of edges, vertices and faces of a polyhedron
convex polyhedra. It states that, for given numbers of triangles, quadrilaterals, pentagons, heptagons, and other polygons other than hexagons, there exists
Eberhard's_theorem
Spherical polyhedron composed of lunes
colored lunes as mirror images. Bisecting each lune into two spherical triangles creates an n {\displaystyle n} -gonal bipyramid, which represents the
Hosohedron
Natural number, composite number
where 14 is the seventh such number. 14 is the number of equilateral triangles that are formed by the sides and diagonals of a regular six-sided hexagon
14_(number)
Solid made by joining an n- and 2n-gon with triangles and pentagons
a cupola but, instead of alternating squares and triangles, they alternate pentagons and triangles around an axis. The pentagonal rotunda is a Johnson
Rotunda_(geometry)
Number whose square is not the sum of 2 non-zero squares
to a nonhypotenuse number cannot form the hypotenuse of a right angle triangle with integer sides. The numbers 1, 2, 3, and 4 are all nonhypotenuse numbers
Nonhypotenuse_number
Concept in mathematics
LCCN 99035678. Snub hexagonal tiling Floret pentagonal tiling Order-3 heptagonal tiling Tilings of regular polygons List of uniform planar tilings Kagome
Snub_trioctagonal_tiling
Size of a geometric arrangement of points
the rth diagonal of Pascal's triangle for r ≥ 0 consists of the figurate numbers for the r-dimensional analogs of triangles (r-dimensional simplices). The
Figurate_number
HEPTAGONAL TRIANGLE
HEPTAGONAL TRIANGLE
HEPTAGONAL TRIANGLE
Boy/Male
Muslim/Islamic
Happy
Girl/Female
Muslim
Glorious
Girl/Female
Hindu
Male
Dutch
, venerable.
Girl/Female
Indian, Modern
A Beautiful Flower
Boy/Male
Spanish
Fresh.
Boy/Male
Latin Greek Shakespearean
Liberator.
Boy/Male
Tamil
Proud, Self-importance
Boy/Male
American, Anglo, Australian, British, Christian, English
From the Sandy Ford; A Crossing
Boy/Male
Australian, German, Turkish
War; Battle
HEPTAGONAL TRIANGLE
HEPTAGONAL TRIANGLE
HEPTAGONAL TRIANGLE
HEPTAGONAL TRIANGLE
HEPTAGONAL TRIANGLE
adv.
In an hexagonal manner.
a.
Developed alike in the directions of the several lateral axes; -- said of crystals of both the tetragonal and hexagonal systems.
n.
Native cadmium sulphide, a mineral occurring in yellow hexagonal crystals, also as an earthy incrustation.
a.
Having six angles; hexagonal.
a.
Having five corners or angles.
a.
Having six sides and six angles; six-sided.
n.
A mineral occurring in pale yellow or brownish hexagonal crystals. It is an arseniate of lead.
a.
Heptagonal.
a.
Having seven angles or sides.
n.
Pure silica, like quartz, but crystallizing in hexagonal tables. It is found in trachyte and similar rocks.
n.
The second stomach of ruminants, in which folds of the mucous membrane form hexagonal cells; -- also called the honeycomb stomach.
n.
A figure which has seven angles; a heptagon.
n.
A mass of hexagonal waxen cells, formed by bees, and used by them to hold their honey and their eggs.
n.
The pentagonal dodecahedron, a common form of pyrite.
a.
Pentagonal.
n.
A variety of mimetite or arseniate of lead in hexagonal prisms of a fine orange yellow.
a.
Consisting of two hexagonal parts united; thus, a dihexagonal pyramid is composed of two hexagonal pyramids placed base to base.
n.
A plane figure consisting of seven sides and having seven angles.
n.
A fluoride of the cerium metals occurring in hexagonal crystals of a pale yellow color. Cf. Fluocerite.