Difference between revisions of "Talk:Lattice:Hexagonal diamond"

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** <math>\left(0,0,\frac{5}{3}l\right),\left(\frac{2\sqrt{6}}{3}l,0,\frac{5}{3}l \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,\frac{5}{3}l\right),\left(\sqrt{6}l,\sqrt{2}l,\frac{5}{3}l\right)</math>
 
** <math>\left(0,0,\frac{5}{3}l\right),\left(\frac{2\sqrt{6}}{3}l,0,\frac{5}{3}l \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,\frac{5}{3}l\right),\left(\sqrt{6}l,\sqrt{2}l,\frac{5}{3}l\right)</math>
 
* <math> 2 \, \mathrm{internal\,\, strut}: \, 1 + 1 = 2</math>
 
* <math> 2 \, \mathrm{internal\,\, strut}: \, 1 + 1 = 2</math>
−
** <math>\left(\frac{a}{2},\frac{b}{2\sqrt{3}},\frac{c}{8}\right),\left(\frac{a}{2},\frac{b}{2\sqrt{3}},\frac{4c}{8}\right)</math>
+
** <math>\left(\frac{\sqrt{6}}{3}l,\frac{\sqrt{2}}{3}l,\frac{1}{3}l\right),\left(\frac{\sqrt{6}}{3}l,\frac{\sqrt{2}}{3}l,\frac{4}{3}l\right)</math>
 
* <math> 4 \, \mathrm{top\,\, layer}: \, \frac{1}{12} + \frac{1}{6} + \frac{1}{12} + \frac{1}{6} = \frac{1}{2}</math>
 
* <math> 4 \, \mathrm{top\,\, layer}: \, \frac{1}{12} + \frac{1}{6} + \frac{1}{12} + \frac{1}{6} = \frac{1}{2}</math>
 
** <math>\left(0,0,\frac{8}{3}l\right),\left(\frac{2\sqrt{6}}{3}l,0,\frac{8}{3}l \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,\frac{8}{3}l\right),\left(\sqrt{6}l,\sqrt{2}l,\frac{8}{3}l\right)</math>
 
** <math>\left(0,0,\frac{8}{3}l\right),\left(\frac{2\sqrt{6}}{3}l,0,\frac{8}{3}l \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,\frac{8}{3}l\right),\left(\sqrt{6}l,\sqrt{2}l,\frac{8}{3}l\right)</math>

Latest revision as of 11:07, 9 January 2018

Absolute

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \, \mathrm{bottom\,\, layer}: \, \frac{1}{12} + \frac{1}{6} + \frac{1}{12} + \frac{1}{6} = \frac{1}{2}}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(0,0,0\right),(a,0,0),\left(\frac{b}{2},\frac{\sqrt{3}b}{2},0\right),\left(a+\frac{b}{2},\frac{\sqrt{3}b}{2},0\right)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \, \mathrm{mid\,\, layer}: \, \frac{1}{6} + \frac{1}{3} + \frac{1}{6} + \frac{1}{3} = 1}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(0,0,\frac{5c}{8}\right),\left(a,0,\frac{5c}{8}\right),\left(\frac{b}{2},\frac{\sqrt{3}b}{2},\frac{5c}{8}\right),\left(a+\frac{b}{2},\frac{\sqrt{3}b}{2},\frac{5c}{8}\right)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \, \mathrm{internal\,\, strut}: \, 1 + 1 = 2}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\frac{a}{2},\frac{b}{2\sqrt{3}},\frac{c}{8}\right),\left(\frac{a}{2},\frac{b}{2\sqrt{3}},\frac{4c}{8}\right)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \, \mathrm{top\,\, layer}: \, \frac{1}{12} + \frac{1}{6} + \frac{1}{12} + \frac{1}{6} = \frac{1}{2}}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(0,0,c\right),(a,0,c),\left(\frac{b}{2},\frac{\sqrt{3}b}{2},c\right),\left(a+\frac{b}{2},\frac{\sqrt{3}b}{2},c\right)}

Distances

For a particle-particle bond-length of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle l} :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a=\frac{2\sqrt{6}}{3}l}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b=a=\frac{2\sqrt{6}}{3}l}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c=\frac{8}{3}l}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{a}{c}=\frac{\sqrt{6}}{4}\approx 0.61237}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{c}{a}=\frac{4}{\sqrt{6}}\approx 1.63299}

Absolute (in terms of particle-particle distance)

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \, \mathrm{bottom\,\, layer}: \, \frac{1}{12} + \frac{1}{6} + \frac{1}{12} + \frac{1}{6} = \frac{1}{2}}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(0,0,0\right),\left(\frac{2\sqrt{6}}{3}l,0,0 \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,0\right),\left(\sqrt{6}l,\sqrt{2}l,0\right)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \, \mathrm{mid\,\, layer}: \, \frac{1}{6} + \frac{1}{3} + \frac{1}{6} + \frac{1}{3} = 1}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(0,0,\frac{5}{3}l\right),\left(\frac{2\sqrt{6}}{3}l,0,\frac{5}{3}l \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,\frac{5}{3}l\right),\left(\sqrt{6}l,\sqrt{2}l,\frac{5}{3}l\right)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \, \mathrm{internal\,\, strut}: \, 1 + 1 = 2}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\frac{\sqrt{6}}{3}l,\frac{\sqrt{2}}{3}l,\frac{1}{3}l\right),\left(\frac{\sqrt{6}}{3}l,\frac{\sqrt{2}}{3}l,\frac{4}{3}l\right)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \, \mathrm{top\,\, layer}: \, \frac{1}{12} + \frac{1}{6} + \frac{1}{12} + \frac{1}{6} = \frac{1}{2}}
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(0,0,\frac{8}{3}l\right),\left(\frac{2\sqrt{6}}{3}l,0,\frac{8}{3}l \right),\left(\frac{\sqrt{6}}{3}l,\sqrt{2}l,\frac{8}{3}l\right),\left(\sqrt{6}l,\sqrt{2}l,\frac{8}{3}l\right)}
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