Icosikaihenagon, or also known as Henicosagon.

21 sided polygon: icosikaihenagon or henicosagon

The sum is 3420 as the equation for every regular polygon is (n-2)*180 when n is number of sides

The term for a 21 sided polygon is an icosikaihenagon. Icosi is the Greek for the numerical 20 and henagon means 1.

Applying systematic polygon names to regular polygons between 20 and 99 sides, a 21-sided polygon would be called an icosikaihenagon.

This is a 21 sided polygon and therefore has 21 angles. NOTE : The name supplied for this polygon is an artificial name and never used in practice. General usage refers to this shape as a 21-gon.

2D PolygonsIcosagon (20 sides)Icosikaihenagon (21 sides)Icosikaidigon (22 sides)Icosikaitrigon (23 sides)Icosikaitetragon (24 sides)Icosikaipentagon (25 sides)Icosikaihexagon (26 sides)Icosikaiheptagon (27 sides)Icosikaioctagon (28 sides)Icosikainoenneagon (29 sides)3D PolyhedraIcosahedron (20 faces)21-29 faces are same as the 2D names but with '-hedron' instead of '-gon' at the end.Also:Isosceles Triangle / Trapezoid(Trapezium)

You can either call them by n-gon for n sides (i.e. 21-gon) or combine a prefix and suffix (i.e. Icosikaihenagon). No. of No. of Sides Name Prefix Name Suffix Sides 20 Icosikai... ...henagon 1 30 Triacontakai... ...digon 2 40 Tetracontakai... ...trigon 3 50 Pentacontakai... ...tetragon 4 60 Hexacontakai... ...pentagon 5 70 Heptacontakai... ...hexagon 6 80 Octacontakai... ...heptagon 7 90 Enneacontakai... ...octagon 8 ...enneagon 9 source: http://www.pubquizhelp.com/sci/polygon.html

Names of Polygons 13 triskaidecagon 14 tetrakaidecagon, tetradecagon 15 pentakaidecagon, pentadecagon 16 hexakaidecagon, hexadecagon 17 heptakaidecagon 18 octakaidecagon 19 enneakaidecagon 20 icosagon 21 icosikaihenagon, icosihenagon 22 icosikaidigon 23 icosikaitrigon 24 icosikaitetragon 25 icosikaipentagon 26 icosikaihexagon 27 icosikaiheptagon 28 icosikaioctagon 29 icosikaienneagon 30 triacontagon 31 triacontakaihenagon 32 triacontakaidigon 33 triacontakaitrigon 34 triacontakaitetragon 35 triacontakaipentagon 36 triacontakaihexagon 37 triacontakaiheptagon 38 triacontakaioctagon 39 triacontakaienneagon 40 tetracontagon 41 tetracontakaihenagon 42 tetracontakaidigon 43 tetracontakaitrigon 44 tetracontakaitetragon 45 tetracontakaipentagon 46 tetracontakaihexagon 47 tetracontakaiheptagon 48 tetracontakaioctagon 49 tetracontakaienneagon 50 pentacontagon ... 60 hexacontagon ... 70 heptacontagon ... 80 octacontagon ... 90 enneacontagon ...

30 triacontagon --- 3 Triangle 4 Quadrilateral 5 pentagon 6 hexagon 7 heptagon septagon 8 octagon 9 nonagon 10 decagon 11 elocagon 12 dodecagon 13 Tridecagon 14 tetrakaidecagon, tetradecagon 15 pentakaidecagon, pentadecagon 16 hexakaidecagon, hexadecagon 17 heptakaidecagon 18 octakaidecagon 19 enneakaidecagon 20 icosagon 21 icosikaihenagon, icosihenagon 22 icosikaidigon 23 icosikaitrigon 24 icosikaitetragon 25 icosikaipentagon 26 icosikaihexagon 27 icosikaiheptagon 28 icosikaioctagon 29 icosikaienneagon 30 triacontagon 31 triacontakaihenagon 32 triacontakaidigon 33 triacontakaitrigon 34 triacontakaitetragon 35 triacontakaipentagon 36 triacontakaihexagon 37 triacontakaiheptagon 38 triacontakaioctagon 39 triacontakaienneagon 40 tetracontagon 41 tetracontakaihenagon 42 tetracontakaidigon 43 tetracontakaitrigon 44 tetracontakaitetragon 45 tetracontakaipentagon 46 tetracontakaihexagon 47 tetracontakaiheptagon 48 tetracontakaioctagon 49 tetracontakaienneagon 50 pentacontagon ... 60 hexacontagon ... 70 heptacontagon ... 80 octacontagon ... 90 enneacontagon ... 100 hectogon, hecatontagon 1000 chiliagon 10000 myriagon

Names of Polygons1 monogon (Monogon and digon can only2 digon be used in rather special3 trigon, triangle circumstances. Trigon and4 tetragon, quadrilateral tetragon are alternatives to5 pentagon triangle and quadrilateral;6 hexagon the adjectival forms trigonal7 heptagon and tetragonal are more common.)8 octagon9 enneagon10 decagon11 hendecagon12 dodecagon13 triskaidecagon14 tetrakaidecagon, tetradecagon15 pentakaidecagon, pentadecagon16 hexakaidecagon, hexadecagon17 heptakaidecagon18 octakaidecagon19 enneakaidecagon20 icosagon21 icosikaihenagon, icosihenagon22 icosikaidigon23 icosikaitrigon24 icosikaitetragon25 icosikaipentagon26 icosikaihexagon27 icosikaiheptagon28 icosikaioctagon29 icosikaienneagon30 triacontagon31 triacontakaihenagon32 triacontakaidigon33 triacontakaitrigon34 triacontakaitetragon35 triacontakaipentagon36 triacontakaihexagon37 triacontakaiheptagon38 triacontakaioctagon39 triacontakaienneagon40 tetracontagon41 tetracontakaihenagon42 tetracontakaidigon43 tetracontakaitrigon44 tetracontakaitetragon45 tetracontakaipentagon46 tetracontakaihexagon47 tetracontakaiheptagon48 tetracontakaioctagon49 tetracontakaienneagon50 pentacontagon ...60 hexacontagon ...70 heptacontagon ...80 octacontagon ...90 enneacontagon ...100 hectogon, hecatontagon1000 chiliagon10000 myriagon

1 monogon (Monogon and digon can only 2 digon be used in rather special 3 trigon, triangle circumstances. Trigon and 4 tetragon, quadrilateral tetragon are alternatives to 5 pentagon triangle and quadrilateral; 6 hexagon the adjectival forms trigonal 7 heptagon and tetragonal are more common.) 8 octagon 9 nonagon 10 decagon 11 hendecagon 12 dodecagon 13 triskaidecagon 14 tetrakaidecagon, tetradecagon 15 pentakaidecagon, pentadecagon 16 hexakaidecagon, hexadecagon 17 heptakaidecagon 18 octakaidecagon 19 enneakaidecagon 20 icosagon 21 icosikaihenagon, icosihenagon 22 icosikaidigon 23 icosikaitrigon 24 icosikaitetragon 25 icosikaipentagon 26 icosikaihexagon 27 icosikaiheptagon 28 icosikaioctagon 29 icosikaienneagon 30 triacontagon 31 triacontakaihenagon 32 triacontakaidigon 33 triacontakaitrigon 34 triacontakaitetragon 35 triacontakaipentagon 36 triacontakaihexagon 37 triacontakaiheptagon 38 triacontakaioctagon 39 triacontakaienneagon 40 tetracontagon 41 tetracontakaihenagon 42 tetracontakaidigon 43 tetracontakaitrigon 44 tetracontakaitetragon 45 tetracontakaipentagon 46 tetracontakaihexagon 47 tetracontakaiheptagon 48 tetracontakaioctagon 49 tetracontakaienneagon 50 pentacontagon ... 60 hexacontagon ... 70 heptacontagon ... 80 octacontagon ... 90 enneacontagon ... 100 hectogon, hecatontagon 1000 chiliagon 10000 myriagon

Polygons: 1 side: (not a polygon) 2 sides: (not a polygon) 3 sides: triangle 4 sides: quadrilateral 5 sides: pentagon 6 sides: hexagon 7 sides: heptagon 8 sides: octagon 9 sides: nonagon 10 sides: decagon 11 sides: hendecagon 12 sides: dodecagon 13 sides: tridecagon 14 sides: tetradecagon 15 sides: pentadecagon 16 sides: hexadecagon 17 sides: heptadecagon 18 sides: octadecagon 19 sides: enneadecagon 20 sides: icosagon 21 sides: icosikaihenagon 22 sides: dikaihenagon 23 sides: trikaihenagon 24 sides: tetrakaihenagon 25 sides: pentakaihenagon 26 sides: hexakaihenagon 27 sides: heptakaihenagon 28 sides: octakaihenagon 29 sides: enneakaihenagon 30 sides: triacontagon Polyhedra (3-d shapes) 1 face:(not a polyhedron) 2 faces:(not a polyhedron) 3 faces:(not a polyhedron) 4 faces: tetrahedron 5 faces: pentahedron 6 faces: hexahedron 7 faces: heptahedron 8 faces: octahedron 9 faces: nonahedron or enneahedron 10 faces: decahedron 11 faces: undecahedron 12 faces: dodecahedron 13 faces: triskaidecahedron 14 faces: tetrakaidecahedron 15 faces: pentakaidecahedron 16 faces: hexakaidecahedron 17 faces: heptakaidecahedron 18 faces: octakaidecahedron 19 faces: enneakaidecahedron 20 faces: icosahedron 21 faces: icosamonohedron 22 faces: icosadihedron 23 faces: icosatrihedron? 24 faces: icosatetrahedron 25 faces: icospentahedron? 26 faces: icosahexahedron 27 faces: icosaheptahedron 28 faces: icosaoctahedron? 29 faces: icosaenneahedron? 30 faces: tricontahedron

Here is an excerpt from John Conway, a very famous mathematician in which he describes how he names the regular polygons.Conway says:"Antreas Hatzipolakis and I worked out a complete system up to the millions from which this is taken, and which has also been "vetted" by several other scholars. The most important of the reasons which make me prefer the "Kai" forms is that they permit these prefixes to be unambiguously parsed even when concatenated, as they are in Kepler's names for certain polyhedra; for example, the icosidodecahedron or (20,12)-hedron, so called because it has 20 faces of one type and 12 of another. Kepler said "this particular triacontakaidihedron I call the icosidodecahedron", a remark showing that he also preferred the Kai forms." Now using this we have: 1 monogon 2 digon 3 trigon, triangle 4 tetragon, quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 enneagon 10 decagon 11 hendecagon 12 dodecagon 13 triskaidecagon 14 tetrakaidecagon, tetradecagon 15 pentakaidecagon, pentadecagon 16 hexakaidecagon, hexadecagon 17 heptakaidecagon 18 octakaidecagon 19 enneakaidecagon 20 icosagon 21 icosikaihenagon, icosihenagon 22 icosikaidigon 23 icosikaitrigon 24 icosikaitetragon 25 icosikaipentagon 26 icosikaihexagon 27 icosikaiheptagon 28 icosikaioctagon 29 icosikaienneagon 30 triacontagon 31 triacontakaihenagon 32 triacontakaidigon 33 triacontakaitrigon 34 triacontakaitetragon 35 triacontakaipentagon 36 triacontakaihexagon 37 triacontakaiheptagon 38 triacontakaioctagon 39 triacontakaienneagon 40 tetracontagon 41 tetracontakaihenagon 42 tetracontakaidigon 43 tetracontakaitrigon 44 tetracontakaitetragon 45 tetracontakaipentagon 46 tetracontakaihexagon 47 tetracontakaiheptagon 48 tetracontakaioctagon 49 tetracontakaienneagon 50 pentacontagon ... 60 hexacontagon ... 70 heptacontagon ... 80 octacontagon ... 90 enneacontagon ... 100 hectogon, hecatontagon 1000 chiliagon 10000 myriagon The "gon" has an interesting etymology: it is ultimately derived from the Greek word "gonu" for "knee", which they transferred to "angle". This word goes straight back to the Indo-European, and is essentially the same in lots of languages: gonu (Greek) genu (Latin) k nee (English) Having said this, if you cannot remember the term, it is safe to use the natural number, n and say an n-gon. So 32 sided polygon can be called a 32-gon and this terminology is widely used and understood among mathematicians. It is very nice to use the correct word, however, often times the price of using it is that many people do not understand what you mean.

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