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    Tristrana prizma

    Tristrana prizma
    Triangular prism.png
    vrsta prizmatični uniformni polieder
    elementi F = 5, E = 9, V = 6,
    (= 2)
    stranske ploskve po straneh 3{4}+2{3}
    Schläflijev simbol t{2,3} ali {3}x{}
    Wythoffov simbol 2
    Coxeter-Dinkinov diagram CDel node 1.png CDel node 1.pngCDel node.png
    simetrija D3h, [3,2],
    (*322) reda 12
    vrtilna grupa D3, [3,2]+,
    (322) reda 6
    sklici U76(a)
    dual trikotna dipiramida
    Triangular prism vertfig.svg
    (slika oglišč)
    4.4.3

    Tristrana prizma je v geometriji prizma s tremi stranskimi ploskvami. To pomeni, da je to polieder s trikotno osnovno ploskvijo.

    To je pentaeder, ki ima dve vzporedni stranski ploskvi. Pri tem pa sta pravokotnici na ostali dve v isti ravnini (ni nujno, da sta vzporedni z ravninami osnovnih ploskev). Te tri stranske ploskve so paralelogrami. Vsi preseki vzporedni z osnovnima ploskvama so enaki trikotniki.

    Vsebina

    Kot polpravilni polieder

    Prostornina

    Prostornina vsake prizme je zmnožek ploščine osnovne ploskve in razdalje med obema osnovnima ploskvama. V tem primeru je osnovna ploskev trikotnik, potrebno je izračunati samo ploščino trikotnika in jo pomnožiti z dolžino prizme:

    kjer je

    Uporaba

    Obstojajo kot celice štirih prizmatičnih uniformnih satovij v treh razsežnostih:

    šeststrano prizmatično satovje
    CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png
    trikotno-šestkotno prizmatično satovje
    CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png
    Snub trikotno-šestkotno prizmatično satovje
    CDel node h.pngCDel 6.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png
    rombitrikotno-šestkotno prizmatično satovje
    CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel infin.pngCDel node.png
    Hexagonal prismatic honeycomb.png Triangular-hexagonal prismatic honeycomb.png Snub triangular-hexagonal prismatic honeycomb.png Rhombitriangular-hexagonal prismatic honeycomb.png

    Obstojajo tudi kot celice številnih štirirazsežnih uniformnih polihoronov vključno z:

    prisekana tetraederska prizma
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png
    prisekana oktaederska prizma
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
    prisekana kubooktederska prizma
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    prisekana ikozaederska prizma
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png
    prisekana ikozidodekaederska prizma
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    Truncated tetrahedral prism.png Truncated octahedral prism.png Truncated cuboctahedral prism.png Truncated icosahedral prism.png Truncated icosidodecahedral prism.png
    runciprisekana 5 celica
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    omniprisekanaomnitruncated 5-cell
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    runciprisekana 16 celica
    CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    omnitruncated tesseract
    CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    4-simplex t013.svg 4-simplex t0123.svg 4-cube t023.svg 4-cube t0123.svg
    runciprisekana 24 celica
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    omniprisekana 24 celica
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    runciprisekana 600 celica
    CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    omniprisekana 120 celica
    CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    24-cell t0123 F4.svg 24-cell t013 F4.svg 120-cell t023 H3.png 120-cell t0123 H3.png

    Sorodni politopi in tlakovanja

    Ta polieder je topološko soroden z zaporedjem uniformnih prisekanih poliedrov s konfiguracijami oglišča (3.2n.2n) in simetrijo Coxeterjeve grupe [n,3].

    Sferna/ravninska
    simetrija
    *232
    [2,3]
    D3h
    *332
    [3,3]
    Td
    *432
    [4,3]
    Oh
    *532
    [5,3]
    Ih
    *632
    [6,3]
    P6m
    *732
    [7,3]
    *832
    [8,3]
    Red
    simetrije
    12 24 48 120
    Coxeter
    Schläfli
    CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{2,3}
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{3,3}
    CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{4,3}
    CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{5,3}
    CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{6,3}
    CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{7,3}
    CDel node 1.pngCDel 8.pngCDel node 1.pngCDel 3.pngCDel node 1.png
    t0,1,2{8,3}
    omniprisekana
    oblika
    Spherical truncated trigonal prism.png
    4.6.4
    Uniform tiling 332-t012.png
    4.6.6
    Uniform tiling 432-t012.png
    4.6.8
    Uniform tiling 532-t012.png
    4.6.10
    Uniform polyhedron-63-t012.png
    4.6.12
    Uniform tiling 73-t012.png
    4.6.14
    Uniform tiling 83-t012.png
    4.6.16

    Štirirazsežni prostor

    tetraederska prizma
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png
    osemstrana prizma
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
    kubooktaederska prizma
    CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
    ikozaederska prizma
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png
    ikozidodekaederska prizma
    CDel node.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png
    prisekana dvanajststrana prizma
    CDel node.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    Tetrahedral prism.png Octahedral prism.png Cuboctahedral prism.png Icosahedral prism.png Icosidodecahedral prism.png Truncated dodecahedral prism.png
    rombiikozidodekaederska prizma
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    rombikubooktaederska prizma
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    prisekana kubična prizma
    CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    Snub dodekaederska prizma
    CDel node h.pngCDel 5.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 2.pngCDel node 1.png
    n-stranska antiprizmatična prizma
    CDel node h.pngCDel n.pngCDel node h.pngCDel 2x.pngCDel node h.pngCDel 2.pngCDel node 1.png
    Rhombicosidodecahedral prism.png Rhombicuboctahedral prism.png Truncated cubic prism.png Snub dodecahedral prism.png Square antiprismatic prism.png
    kantelirana 5 celica
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
    kantiprisekana 5 celica
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
    runcinirana 5 celica
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
    runciprisekana 5 celica
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
    kantelirani teserakt
    CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
    kantiprisekani teserakt
    CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
    runcinirani teserakt
    CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
    runciprisekani teserakt
    CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
    4-simplex t02.svg 4-simplex t012.svg 4-simplex t03.svg 4-simplex t013.svg 4-cube t02.svg 4-cube t012.svg 4-cube t03.svg 4-cube t013.svg
    kantelirana 24 celica
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
    kantiprisekana 24 celica
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
    runcinirana 24 celica
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
    runciprisekana 24 celica
    CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
    kantelirana 120 celica
    CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
    kantiprisekana 120 celica
    CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
    runcinirana 120 celica
    CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
    runciprisekana 120 celica
    CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
    24-cell t02 F4.svg 24-cell t012 F4.svg 24-cell t03 F4.svg 24-cell t013 F4.svg 120-cell t02 H3.png 120-cell t012 H3.png 120-cell t03 H3.png 120-cell t013 H3.png

    Glej tudi

    Družina uniformnih prizem
    mnogokotnik Triangular prism.png Tetragonal prism.png Pentagonal prism.png Hexagonal prism.png Prism 7.png Octagonal prism.png Prism 9.png Decagonal prism.png Hendecagonal prism.png Dodecagonal prism.png   Circular cylinder rh.svg
    Coxeter-
    Dinkin
    CDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 5.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 6.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 7.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 8.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 9.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 10.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 11.pngCDel node.pngCDel 2.pngCDel node 1.png CDel node 1.pngCDel 12.pngCDel node.pngCDel 2.pngCDel node 1.png   CDel node 1.pngCDel infin.pngCDel node.pngCDel 2.pngCDel node 1.png
    CDel node 1.pngCDel infin.pngCDel node 1.pngCDel 2.pngCDel node 1.png
    tlakovanje Spherical triangular prism.png Spherical square prism.png Spherical pentagonal prism.png Spherical hexagonal prism.png Spherical heptagonal prism.png Spherical octagonal prism.png Spherical decagonal prism.png   Infinite prism tiling.png
    konfiguracija 3.4.4 4.4.4 5.4.4 6.4.4 7.4.4 8.4.4 9.4.4 10.4.4 11.4.4 12.4.4 ... ∞.4.4
    Skupina kupol
    2 3 4 5 6
    Triangular prism wedge.png
    diagonalna kupola
    Triangular cupola.png
    trikotna kupola
    Square cupola.png
    kvadratna kupola
    Pentagonal cupola.png
    petkotna kupola
    Hexagonal cupola flat.png
    šestkotna kupola
    (ravna oblika)

    Zunanje povezave