WikiDer > Polihedrli dihedral burchaklar jadvali
Table of polyhedron dihedral angles
The dihedral burchaklar uchun o'tish davri ko'pburchak:
| Rasm | Ism | Schläfli belgi | Vertex / Face konfiguratsiya | aniq dihedral burchak (radianlar) | dihedral burchak - aniq qalin, boshqa taxminiy (daraja) |
|---|---|---|---|---|---|
| Platonik qattiq moddalar (muntazam qavariq) | |||||
 | Tetraedr | {3,3} | (3.3.3) | arkos (1/3) | 70.53° |
 | Geksaedr yoki Kub | {4,3} | (4.4.4) | π/2 | 90° |
 | Oktaedr | {3,4} | (3.3.3.3) | π - arkoslar (1/3) | 109.47° |
 | Dodekaedr | {5,3} | (5.5.5) | π - Arktan (2) | 116.57° |
 | Ikosaedr | {3,5} | (3.3.3.3.3) | π - arkoslar (√5/3) | 138.19° |
| Kepler-Poinsot qattiq moddalari (muntazam konveks) | |||||
 | Kichik stellated dodecahedron | {5/2,5} | (5/2.5/2.5/2.5/2.5/2) | π - Arktan (2) | 116.56° |
 | Ajoyib dodekaedr | {5,5/2} | (5.5.5.5.5)/2 | Arktan (2) | 63.435° |
 | Ajoyib yulduzli dodekaedr | {5/2,3} | (5/2.5/2.5/2) | Arktan (2) | 63.435° |
 | Ajoyib ikosaedr | {3,5/2} | (3.3.3.3.3)/2 | arcsin (2/3) | 41.810° |
| Quasiregular polyhedra (Muntazam ravishda tuzatilgan) | |||||
 | Tetratetraedr | r {3,3} | (3.3.3.3) | π - arkoslar (1/3) | 109.47° |
 | Kubokededr | r {3,4} | (3.4.3.4) | π - arkoslar (1/√3) | 125.264° |
 | Ikozidodekaedr | r {3,5} | (3.5.3.5) | 142.623° | |
 | O'n ikki kunlik | r {5/2,5} | (5.5/2.5.5/2) | π - Arktan (2) | 116.56° |
 | Ajoyib ikosidodekaedr | r {5/2,3} | (3.5/2.3.5/2) | 37.377° | |
| Ditrigonal ko'p qirrali | |||||
 | Kichik ditrigonal ikosidodekaedr | a {5,3} | (3.5/2.3.5/2.3.5/2) | ||
 | Ditrigonal dodekadodekaedr | b {5,5/2} | (5.5/3.5.5/3.5.5/3) | ||
 | Ditrigonal ikosidodekaedr | c {3,5/2} | (3.5.3.5.3.5)/2 | ||
| Hemipolyhedra | |||||
 | Tetrahemigeksaedr | o {3,3} | (3.4.3/2.4) | 54.73° | |
 | Kubogemioktaedr | o {3,4} | (4.6.4/3.6) | 54.73° | |
 | Oktahemiyoktaedr | o {4,3} | (3.6.3/2.6) | 70.53° | |
 | Kichik dodekaxemidodekaedr | o {3,5} | (5.10.5/4.10) | 26.063° | |
 | Kichik ikosihemidodekaedr | o {5,3} | (3.10.3/2.10) | 116.56° | |
 | Ajoyib dodekemikozedr | o {5/2,5} | (5.6.5/4.6) | ||
 | Kichik dodekemikozedr | o {5,5/2} | (5/2.6.5/3.6) | ||
 | Ajoyib ikosihemidodekaedr | o {5/2,3} | (3.10/3.3/2.10/3) | ||
 | Ajoyib dodekaxemidodekaedr | o {3,5/2} | (5/2.10/3.5/3.10/3) | ||
| Quasiregular dual qattiq moddalar | |||||
| Rombik olti burchakli (Ikki tetratetraedr) | — | V (3.3.3.3) | π − π/2 | 90° |
 | Rombik dodekaedr (Kuboktaedrning juftligi) | — | V (3.4.3.4) | π − π/3 | 120° |
 | Rombik triakontaedr (Ikosidodekaedrning ikkitasi) | — | V (3.5.3.5) | π − π/5 | 144° |
 | Medial rombik triakontaedr (Ikki dodekododekaedr) | — | V (5.5/2.5.5/2) | π − π/3 | 120° |
 | Ajoyib rombik triakontaedr (Katta ikosidodekaedrning juftligi) | — | V (3.5/2.3.5/2) | π − 2π/5 | 72° |
| Ditrigonal ko'p qirrali juftliklar | |||||
 | Kichik triambik ikosaedr (Kichik ditrigonal ikosidodekaedrning juftligi) | — | V (3.5/2.3.5/2.3.5/2) | ||
 | Medial triambik ikosaedr (Ikki ditrigonal dodekadodekaedr) | — | V (5.5/3.5.5/3.5.5/3) | ||
 | Buyuk triambik ikosaedr (Katta ditrigonal ikosidodekaedrning juftligi) | — | V(3.5.3.5.3.5)/2 | ||
| Gemipolihedraning ikkiliklari | |||||
 | Tetrahemigeksakron (Tetrahemikeksaedrning juftligi) | — | V (3.4.)3/2.4) | π − π/2 | 90° |
 | Geksaxemioktakron (Kubogemioktaedrning juftligi) | — | V (4.6.)4/3.6) | π − π/3 | 120° |
| Oktahemioktakron (Oktahemioktahedrning ikkilamchi xususiyati) | — | V (3.6.)3/2.6) | π − π/3 | 120° |
 | Kichik dodekaxemidodekakron (Kichik dodekaxemidodekakronning ikkitasi) | — | V (5.10.)5/4.10) | π − π/5 | 144° |
| Kichik icosihemidodekakron (Kichik ikosihemidodekakronning ikkitasi) | — | V (3.10.)3/2.10) | π − π/5 | 144° |
 | Ajoyib dodekemikosakron (Katta dodekemikozedrning juftligi) | — | V (5.6.)5/4.6) | π − π/3 | 120° |
| Kichik dodekemikosakron (Ikki kichik dodekemikozedr) | — | V (5/2.6.5/3.6) | π − π/3 | 120° |
 | Ajoyib icosihemidodekakron (Buyuk icosihemidodekakronning juftligi) | — | V (3.10/3.3/2.10/3) | π − 2π/5 | 72° |
| Ajoyib dodekaxemidodekakron (Katta dodekaxemidodekakronning juftligi) | — | V (5/2.10/3.5/3.10/3) | π − 2π/5 | 72° |
Adabiyotlar
- Kokseter, Muntazam Polytopes (1963), Makmillan kompaniyasi
- Muntazam Polytopes, (3-nashr, 1973), Dover nashri, ISBN 0-486-61480-8 (Jadval I: Muntazam Polytopes, (i) Oddiy kosmosdagi to'qqizta muntazam ko'pburchak {p, q})
- Uilyams, Robert (1979). Tabiiy inshootning geometrik asosi: dizaynning manba kitobi. Dover Publications, Inc. ISBN 0-486-23729-X. (3-7 dan 3-9 gacha)
- Vayshteyn, Erik V. "Bir xil poliedr". MathWorld.