"of a regular hendecagon is still impossible even with the usage of an angle trisector. It can, however, be constructed via neusis construction and also via two-fold origami. Close approximations to the regular hendecagon can be constructed, however. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a unit circle as being 14/25 units long. The following construction description is given by T. Drummond from 1800: On a unit circle: The ""regular hendecagon"" has Dih symmetry, order 22. Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih, and 2"
"Hexadecagon In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. A ""regular hexadecagon"" is a hexadecagon in which all angles are equal and all sides are congruent. Its Schläfli symbol is {16} and can be constructed as a truncated octagon, t{8}, and a twice-truncated square tt{4}. A truncated hexadecagon, t{16}, is a triacontadigon, {32}. As 16 = 2 (a power of two), a regular hexadecagon is constructible using compass and straightedge: this was already known to ancient Greek mathematicians. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any"
"Hendecahedron A hendecahedron (or undecahedron) is a polyhedron with 11 faces. There are numerous topologically distinct forms of a hendecahedron, for example the decagonal pyramid, and enneagonal prism. Three forms are Johnson solids: augmented hexagonal prism, biaugmented triangular prism, and elongated pentagonal pyramid. Two classes, the bisymmetric and the sphenoid hendecahedra, are space-filling. The name of hendecahedron is based on its meaning. Hen- represents one. Deca represents ten, and then combined with the polyhedron suf-hedron, it is Hendecahedron. In all the convex hendecahedrons, there are a total of 440,564 convex ones with distinct differences in topology. There are significant differences"
"(Two polyhedra are ""topologically distinct"" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) Hendecahedron A hendecahedron (or undecahedron) is a polyhedron with 11 faces. There are numerous topologically distinct forms of a hendecahedron, for example the decagonal pyramid, and enneagonal prism. Three forms are Johnson solids: augmented hexagonal prism, biaugmented triangular prism, and elongated pentagonal pyramid. Two classes, the bisymmetric and the sphenoid hendecahedra, are space-filling. The name of hendecahedron is based on"
"Hexagon In geometry, a hexagon (from Greek ἕξ ""hex"", ""six"" and γωνία, ""gonía"", ""corner, angle"") is a six-sided polygon or 6-gon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. A ""regular hexagon"" has Schläfli symbol {1} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius"
"Hectogon In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon. The sum of any hectogon's interior angles is 17640 degrees. A ""regular hectogon"" is represented by Schläfli symbol {100} and can be constructed as a truncated pentacontagon, t{50}, or a twice-truncated icosipentagon, tt{25}. One interior angle in a regular hectogon is 176°, meaning that one exterior angle would be 3°. The area of a regular hectogon is (with ) and its inradius is The circumradius of a regular hectogon is Because 100 = 2 × 5, the number of sides contains a ""repeated"" Fermat prime (the number"
"Enneacontahexagon In geometry, an enneacontahexagon (or enneacontakaihexagon) or 96-gon is a ninety-six-sided polygon. The sum of any enneacontahexagons's interior angles is 16920 degrees. The ""regular enneacontahexagon"" is represented by Schläfli symbol {96} and can also be constructed as a truncated tetracontaoctagon, t{48}, or a twice-truncated icositetragon, tt{24}, or a thrice-truncated dodecagon, ttt{12}, or a fourfold-truncated hexagon, tttt{6}, or a fivefold-truncated triangle, }. One interior angle in a regular enneacontahexagon is 176°, meaning that one exterior angle would be 3°. The area of a regular enneacontahexagon is: (with ""t"" = edge length) The enneacontahexagon appeared in Archimedes' polygon approximation of pi,"
"Hendecagram In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name ""hendecagram"" combines a Greek numeral prefix, ""hendeca-"", with the Greek suffix ""-gram"". The ""hendeca-"" prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning ""eleven"". The ""-gram"" suffix derives from γραμμῆς (""grammēs"") meaning a line. There are four regular hendecagrams, which can be described by the notation Since 11 is prime, all hendecagrams are star polygons and not compound figures. As with all odd regular polygons and star polygons whose orders are not products of distinct Fermat primes, the"
"Heptagon In geometry, a heptagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using ""sept-"" (an elision of """", a Latin-derived numerical prefix, rather than """", a Greek-derived numerical prefix) together with the Greek suffix ""-agon"" meaning angle. A regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians (128 degrees). Its Schläfli symbol is {7}. The area (""A"") of a regular heptagon of side length ""a"" is given by: This can be seen by subdividing the unit-sided heptagon into seven triangular ""pie slices"" with vertices"
"Hexadecahedron A hexadecahedron (or hexakaidecahedron) is a polyhedron with 16 faces. No hexadecahedron is regular; hence, the name is ambiguous. There are numerous topologically distinct forms of a hexadecahedron, for example the pentadecagonal pyramid, tetradecagonal prism and heptagonal antiprism. There are 387,591,510,244 topologically distinct ""convex"" hexadecahedra, excluding mirror images, having at least 10 vertices. (Two polyhedra are ""topologically distinct"" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) There are 302,404 self-dual hexadecahedron, 1476"
"Hexacontatetragon In geometry, a hexacontatetragon (or hexacontakaitetragon) or 64-gon is a sixty-four-sided polygon. (In Greek, the prefix hexaconta- means 60 and tetra- means 4.) The sum of any hexacontatetragon's interior angles is 11160 degrees. The ""regular hexacontatetragon"" can be constructed as a truncated triacontadigon, t{32}, a twice-truncated hexadecagon, tt{16}, a thrice-truncated octagon, ttt{8}, a fourfold-truncated square, tttt{4}, and a fivefold-truncated digon, }. One interior angle in a regular hexacontatetragon is 174°, meaning that one exterior angle would be 5°. The area of a regular hexacontatetragon is (with ) and its inradius is The circumradius of a regular hexacontatetragon is Since"
"Hendecagonal antiprism In geometry, the hendecagonal antiprism is the ninth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals. In the case of a regular 11-sided base, one usually considers the case where its copy is twisted by an angle 180°/""n"". Extra regularity is obtained by the line connecting the base centers being perpendicular to the base planes, making it a right antiprism. As faces, it"
"of the Virgin"" has 16 sides, elaborating on an eight-sided tower in a previous painting by Pietro Perugino. Hexadecagrams (16-sided star polygons) are included in the Girih patterns in the Alhambra. In the Philippines, in local carnivals (peryahan), Ferris Wheels with maximum of 16 seats or gondolas An octagonal star can be seen as a concave hexadecagon: Hexadecagon In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. A ""regular hexadecagon"" is a hexadecagon in which all angles are equal and all sides are congruent. Its Schläfli symbol is {16} and can be constructed as a"
"{96/37}, {96/41}, {96/43}, and {96/47}, as well as 32 compound star figures with the same vertex configuration. Enneacontahexagon In geometry, an enneacontahexagon (or enneacontakaihexagon) or 96-gon is a ninety-six-sided polygon. The sum of any enneacontahexagons's interior angles is 16920 degrees. The ""regular enneacontahexagon"" is represented by Schläfli symbol {96} and can also be constructed as a truncated tetracontaoctagon, t{48}, or a twice-truncated icositetragon, tt{24}, or a thrice-truncated dodecagon, ttt{12}, or a fourfold-truncated hexagon, tttt{6}, or a fivefold-truncated triangle, }. One interior angle in a regular enneacontahexagon is 176°, meaning that one exterior angle would be 3°. The area of a"
"and {100/49}, as well as 30 regular star figures with the same vertex configuration. Hectogon In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon. The sum of any hectogon's interior angles is 17640 degrees. A ""regular hectogon"" is represented by Schläfli symbol {100} and can be constructed as a truncated pentacontagon, t{50}, or a twice-truncated icosipentagon, tt{25}. One interior angle in a regular hectogon is 176°, meaning that one exterior angle would be 3°. The area of a regular hectogon is (with ) and its inradius is The circumradius of a regular hectogon is Because 100 ="
"Hexacontagon In geometry, a hexacontagon or hexecontagon or 60-gon is a sixty-sided polygon. The sum of any hexacontagon's interior angles is 10440 degrees. A ""regular hexacontagon"" is represented by Schläfli symbol {60} and also can be constructed as a truncated triacontagon, t{30}, or a twice-truncated pentadecagon, tt{15}. A truncated hexacontagon, t{60}, is a 120-gon, {120}. One interior angle in a regular hexacontagon is 174°, meaning that one exterior angle would be 6°. The area of a regular hexacontagon is (with ) and its inradius is The circumradius of a regular hexacontagon is This means that the trigonometric functions of π/60"
"Enneadecahedron A enneadecahedron (or enneakaidecahedron) is a polyhedron with 19 faces. No enneadecahedron is regular; hence, the name is ambiguous. There are numerous topologically distinct forms of an enneadecahedron, for example the octadecagonal (18-sided) pyramid, or the heptadecagonal (17-sided) prism; the latter is the only convex enneadecahedron with all regular polygonal faces. There are many topologically distinct ""convex"" enneadecahedra, excluding mirror images, having at least 12 vertices. (Two polyhedra are ""topologically distinct"" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges"
"based on a Petrie polygon projection of a 8-cube, with 28 of 1792 faces. The list enumerates the number of solutions as 1232944, including up to 16-fold rotations and chiral forms in reflection. A skew hexadecagon is a skew polygon with 24 vertices and edges but not existing on the same plane. The interior of such an hexadecagon is not generally defined. A ""skew zig-zag hexadecagon"" has vertices alternating between two parallel planes. A regular skew hexadecagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew hexadecagon and can be seen in the vertices and"
"and reduced thrust after the points of the star were burned away, at approximately the same time as the rocket passed the sound barrier. Hendecagram In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name ""hendecagram"" combines a Greek numeral prefix, ""hendeca-"", with the Greek suffix ""-gram"". The ""hendeca-"" prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning ""eleven"". The ""-gram"" suffix derives from γραμμῆς (""grammēs"") meaning a line. There are four regular hendecagrams, which can be described by the notation Since 11 is prime, all hendecagrams are star"
"the same length. The ratio of a diagonal to a side is the golden ratio, formula_5 A regular hexagon has nine diagonals: the six shorter ones are equal to each other in length; the three longer ones are equal to each other in length and intersect each other at the center of the hexagon. The ratio of a long diagonal to a side is 2. A regular heptagon has 14 diagonals. The seven shorter ones equal each other, and the seven longer ones equal each other. The reciprocal of the side equals the sum of the reciprocals of a short"
"Truncated hexagonal tiling In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each vertex. As the name implies this tiling is constructed by a truncation operation applies to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations. It is given an extended Schläfli symbol of ""t""{6,3}. Conway calls it a truncated hextille, constructed as a truncation operation applied to a hexagonal tiling (hextille). There are 3 regular and 8 semiregular tilings in the plane. There is"
"Truncated pentagonal hexecontahedron The truncated pentagonal hexecontahedron is a convex polyhedron with 72 faces: 60 hexagons and 12 pentagons triangular, with 210 edges, and 140 vertices. Its dual is the pentakis snub dodecahedron. It is Goldberg polyhedron {5+,3} in the icosahedral family, with chiral symmetry. The relationship between pentagons steps into 2 hexagons away, and then a turn with one more step. It is a Fullerene C140. It is explicitly called a ""pentatruncated pentagonal hexecontahedron"" since only the valence-5 vertices of the pentagonal hexecontahedron are truncated. Its topology can be constructed in Conway polyhedron notation as ""t5gD"" and more simply"
"Tetradecagon In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon. A ""regular tetradecagon"" has Schläfli symbol {14} and can be constructed as a quasiregular truncated heptagon, t{7}, which alternates two types of edges. The area of a regular tetradecagon of side length ""a"" is given by As 14 = 2 × 7, a regular tetradecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis with use of the angle trisector, or with a marked ruler, as it in the following two examples showned. The animation below gives an approximation of about 0.05°"
"along with the hexagon (6-gon), dodecagon (12-gon), icositetragon (24-gon), and tetracontaoctagon (48-gon). Since 96 = 2 × 3, a regular enneacontahexagon is constructible using a compass and straightedge. As a truncated tetracontaoctagon, it can be constructed by an edge-bisection of a regular tetracontaoctagon. The ""regular enneacontahexagon"" has Dih symmetry, order 192. There are 11 subgroup dihedral symmetries: (Dih, Dih, Dih, Dih, Dih), (Dih, Dih, Dih, Dih, Dih and Dih), and 12 cyclic group symmetries: (Z, Z, Z, Z, Z, Z), (Z, Z, Z, Z, Z, and Z). These 24 symmetries can be seen in 34 distinct symmetries on the enneacontahexagon."
"are added to the 20 triangular faces that do not share an edge with a pentagon. The pyramid heights are adjusted to make them coplanar with the other 60 triangular faces of the snub dodecahedron. The result is the pentagonal hexecontahedron. The faces are irregular pentagons with two long edges and three short edges. The ratio of edge lengths is about 1:1.7498525667362. The faces have four obtuse angles of about 118.13662 degrees each, and one acute angle (between the two long edges) of about 67.45351 degrees. The dihedral angle is about 153.178732558 degrees between all faces. Note that the face"
"of the hexaflexagons into 30-60-90 right triangles yields the dodecaflexagons. In its flat state, the pentaflexagon looks much like the Chrysler logo: a regular pentagon divided from the center into five isosceles triangles, with angles 72-54-54. Because of its fivefold symmetry, the pentaflexagon cannot be folded in half. However, a complex series of flexes results in its transformation from displaying sides one and two on the front and back, to displaying its previously hidden sides three and four. By further dividing the 72-54-54 triangles of the pentaflexagon into 36-54-90 right triangles produces one variation of the 10-sided decaflexagon. The pentaflexagon"
"hexadecagon is 2520 degrees. The area of a regular hexadecagon with edge length ""t"" is Because the hexadecagon has a number of sides that is a power of two, its area can be computed in terms of the circumradius ""R"" by truncating Viète's formula: Since the area of the circumcircle is formula_3 the regular hexadecagon fills approximately 97.45% of its circumcircle. The ""regular hexadecagon"" has Dih symmetry, order 32. There are 4 dihedral subgroups: Dih, Dih, Dih, and Dih, and 5 cyclic subgroups: Z, Z, Z, Z, and Z, the last implying no symmetry. On the regular hexadecagon, there are"
"faces and vertices. After being distorted, it will get different characteristics. The most symmetric hendecahedron is the double symmetric hendecahedron. Because it has two symmetric faces, it is named as the double symmetric hendecahedron. In the chemistry, after removing all 18 sides in borane hydrogen ions ([BH]), it is an Octadecahedron. If making a perpendicular to the center of gravity to the surface of a boron atom, a new polyhedron is constructed, which is 18 surface structures of the dual polyhedron, also one of hendecahedrons. There are 440,564 topologically distinct ""convex"" hendecahedra, excluding mirror images, having at least 8 vertices."
"Heptadecahedron A heptadecahedron (or heptakaidecahedron) is a polyhedron with 17 faces. No heptadecahedron is regular; hence, the name is ambiguous. There are numerous topologically distinct forms of a heptadecahedron, for example the hexadecagonal pyramid and pentadecagonal prism. There are 6,415,851,530,241 topologically distinct ""convex"" heptadecahedra, excluding mirror images, having at least 11 vertices. (Two polyhedra are ""topologically distinct"" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) The infinite Laves graph has convex heptadecahedral Voronoi"
"or the angles between edges or faces.) Enneadecahedron A enneadecahedron (or enneakaidecahedron) is a polyhedron with 19 faces. No enneadecahedron is regular; hence, the name is ambiguous. There are numerous topologically distinct forms of an enneadecahedron, for example the octadecagonal (18-sided) pyramid, or the heptadecagonal (17-sided) prism; the latter is the only convex enneadecahedron with all regular polygonal faces. There are many topologically distinct ""convex"" enneadecahedra, excluding mirror images, having at least 12 vertices. (Two polyhedra are ""topologically distinct"" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other"
"Heptahedron A heptahedron (plural: heptahedra) is a polyhedron having seven sides, or faces. A heptahedron can take a surprising number of different basic forms, or topologies. Probably most familiar are the hexagonal pyramid and the pentagonal prism. Also notable is the tetrahemihexahedron, whose seven faces form a rudimentary projective plane. No heptahedra are regular. There are 34 topologically distinct ""convex"" heptahedra, excluding mirror images. (Two polyhedra are ""topologically distinct"" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles"
"Pentagonal hexecontahedron In geometry, a pentagonal hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or ""enantiomorphs"") of each other. It has 92 vertices that span 60 pentagonal faces. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices. The pentagonal hexecontahedron can be constructed from a snub dodecahedron without taking the dual. Pentagonal pyramids are added to the 12 pentagonal faces of the snub dodecahedron, and triangular pyramids"
"Triacontadigon In geometry, a triacontadigon (or triacontakaidigon) or 32-gon is a thirty-two-sided polygon. In Greek, the prefix triaconta- means 30 and di- means 2. The sum of any triacontadigon's interior angles is 5400 degrees. An older name is tricontadoagon. Another name is icosidodecagon, suggesting a (20 and 12)-gon, in parallel to the 32-faced icosidodecahedron, which has 20 triangles and 12 pentagons. The ""regular triacontadigon"" can be constructed as a truncated hexadecagon, t{16}, a twice-truncated octagon, tt{8}, and a thrice-truncated square. A truncated triacontadigon, t{32}, is a hexacontatetragon, {64}. One interior angle in a regular triacontadigon is 168°, meaning that one"