OpenDEM 1: 1 revision imported from :wikipedia:en:Template:Regular_convex_4-polytopes

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1 revision imported from wikipedia:en:Template:Regular_convex_4-polytopes

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wikipedia:en>HaToll: Undid revision 1292388333 by HaToll (talk)

2025-05-27T09:15:46Z

Undid revision 1292388333 by HaToll (talk)

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{| class="wikitable mw-collapsible {{{collapsestate|mw-collapsed}}}" style="white-space:nowrap;text-align:center;"
!colspan=8|[[Regular 4-polytopes|Regular convex 4-polytopes]] {{#if:{{{radius|}}}|of radius {{{radius|}}}|}}
|-
!style="text-align:right;"|[[Coxeter_group|Symmetry group]]
|[[Tetrahedral symmetry|A4]]
|colspan=2|[[Hyperoctahedral_group|B4]]
|[[F4_(mathematics)|F4]]
|colspan=2|[[H4_polytope|H4]]
|-
!style="vertical-align:top;text-align:right;"|Name
|style="vertical-align:top;"|[[5-cell]] 
Hyper-[[tetrahedron]] 
5-point
|style="vertical-align:top;"|[[16-cell]] 
Hyper-[[octahedron]] 
8-point
|style="vertical-align:top;"|[[8-cell]] 
Hyper-[[cube]] 
16-point
|style="vertical-align:top;"|[[24-cell]] 
 24-point
|style="vertical-align:top;"|[[600-cell]] 
Hyper-[[Regular icosahedron|icosahedron]] 
120-point
|style="vertical-align:top;"|[[120-cell]] 
Hyper-[[Regular dodecahedron|dodecahedron]] 
600-point
|-
!style="text-align:right;"|[[Schläfli symbol]]
|{3, 3, 3}
|{3, 3, 4}
|{4, 3, 3}
|{3, 4, 3}
|{3, 3, 5}
|{5, 3, 3}
|-
!style="text-align:right;"|[[Coxeter diagram|Coxeter mirrors]]
|{{Coxeter–Dynkin diagram|node_1|3|node|3|node|3|node}}
|{{Coxeter–Dynkin diagram|node_1|3|node|3|node|4|node}}
|{{Coxeter–Dynkin diagram|node_1|4|node|3|node|3|node}}
|{{Coxeter–Dynkin diagram|node_1|3|node|4|node|3|node}}
|{{Coxeter–Dynkin diagram|node_1|3|node|3|node|5|node}}
|{{Coxeter–Dynkin diagram|node_1|5|node|3|node|3|node}}
|-
!style="text-align:right;"|Mirror dihedrals
|{{sfrac|𝝅|3}} {{sfrac|𝝅|3}} {{sfrac|𝝅|3}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}}
|{{sfrac|𝝅|3}} {{sfrac|𝝅|3}} {{sfrac|𝝅|4}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}}
|{{sfrac|𝝅|4}} {{sfrac|𝝅|3}} {{sfrac|𝝅|3}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}}
|{{sfrac|𝝅|3}} {{sfrac|𝝅|4}} {{sfrac|𝝅|3}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}}
|{{sfrac|𝝅|3}} {{sfrac|𝝅|3}} {{sfrac|𝝅|5}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}}
|{{sfrac|𝝅|5}} {{sfrac|𝝅|3}} {{sfrac|𝝅|3}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}} {{sfrac|𝝅|2}}
|-
!style="vertical-align:top;text-align:right;"|Graph
|[[Image:4-simplex t0.svg|120px]]
|[[Image:4-cube t3.svg|120px]]
|[[Image:4-cube t0.svg|120px]]
|[[Image:24-cell t0 F4.svg|120px]]
|[[Image:600-cell graph H4.svg|120px]]
|[[Image:120-cell graph H4.svg|120px]]
|-
!style="text-align:right;"|Vertices
|5 tetrahedral
|8 octahedral
|16 tetrahedral
|24 cubical
|120 icosahedral
|600 tetrahedral
|-
!style="vertical-align:top;text-align:right;"|[[120-cell#Chords|Edges]]
|10 triangular
|24 square
|32 triangular
|96 triangular
|720 pentagonal
|1200 triangular
|-
!style="vertical-align:top;text-align:right;"|Faces
|10 triangles
|32 triangles
|24 squares
|96 triangles
|1200 triangles
|720 pentagons
|-
!style="vertical-align:top;text-align:right;"|Cells
|5 tetrahedra
|16 tetrahedra
|8 cubes
|24 octahedra
|600 tetrahedra
|120 dodecahedra
|-
!style="vertical-align:top;text-align:right;"|[[600-cell#Clifford parallel cell rings|Tori]]
|1 [[5-cell#Boerdijk–Coxeter helix|5-tetrahedron]]
|2 [[16-cell#Helical construction|8-tetrahedron]]
|2 [[8-cell#Construction|4-cube]]
|4 [[24-cell#Cell rings|6-octahedron]]
|20 [[600-cell#Boerdijk–Coxeter helix rings|30-tetrahedron]]
|12 [[120-cell#Intertwining rings|10-dodecahedron]]
|-
!style="vertical-align:top;text-align:right;"|Inscribed
|120 in 120-cell
|675 in 120-cell
|2 16-cells
|3 8-cells
|25 24-cells
|10 600-cells
|-
!style="vertical-align:top;text-align:right;"|[[Great circle|Great polygons]]
|
|2 [[16-cell#Coordinates|squares]] x 3
|4 rectangles x 4
|4 [[24-cell#Hexagons|hexagons]] x 4
|12 [[600-cell#Geodesics|decagons]] x 6
|100 [[120-cell#Chords|irregular hexagons]] x 4
|-
!style="vertical-align:top;text-align:right;"|[[Petrie polygon]]s
|1 [[5-cell#Boerdijk–Coxeter helix|pentagon]] x 2
|1 [[16-cell#Helical construction|octagon]] x 3
|2 [[Octagon#Skew octagon|octagon]]s x 4
|2 [[Dodecagon#Skew dodecagon|dodecagon]]s x 4
|4 [[30-gon#Petrie polygons|30-gon]]s x 6
|20 [[30-gon#Petrie polygons|30-gon]]s x 4
|-
!style="vertical-align:top;text-align:right;"|{{#ifeq:{{{radius|}}}|1|[[24-cell#Hexagons|Long radius]]|{{#ifeq:{{{radius|}}}|{{radic|2}}|[[24-cell#Squares|Long radius]]|Long radius}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2}</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2}</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2}</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2}</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2}</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2}</math>}}}}
|-
!style="vertical-align:top;text-align:right;"|Edge length
|{{#ifeq:{{{radius|1}}}|1|<math>\sqrt{\tfrac{5}{2}} \approx 1.581</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{5} \approx 2.236</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\sqrt{2} \approx 1.414</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>2</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2} \approx 1.414</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{2} \approx 1.414</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{1}{\phi} \approx 0.618</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\sqrt{2}}{\phi} \approx 0.874</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{1}{\phi^2\sqrt{2}} \approx 0.270</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>2-\phi \approx 0.382</math>}}}}
|-
!style="vertical-align:top;text-align:right;"|Short radius
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{1}{4}</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\sqrt{2}}{4} \approx 0.354</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{1}{2}</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\sqrt{2}}{2} \approx 0.707</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{1}{2}</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\sqrt{2}}{2} \approx 0.707</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\sqrt{\tfrac{1}{2}} \approx 0.707</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>1</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\sqrt{\tfrac{\phi^4}{8}} \approx 0.926</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{\tfrac{\phi^4}{4}} \approx 1.309</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\sqrt{\tfrac{\phi^4}{8}} \approx 0.926</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\sqrt{\tfrac{\phi^4}{4}} \approx 1.309</math>}}}}
|-
!style="vertical-align:top;text-align:right;"|Area
|{{#ifeq:{{{radius|1}}}|1|<math>10\left(\tfrac{5\sqrt{3}}{8}\right) \approx 10.825</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>10\left(\tfrac{5\sqrt{3}}{4}\right) \approx 21.651</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>32\left(\sqrt{\tfrac{3}{4}}\right) \approx 27.713</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>32\left(\sqrt{3}\right) \approx 55.425</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>24</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>48</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>96\left(\sqrt{\tfrac{3}{16}}\right) \approx 41.569</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>96\left(\sqrt{\tfrac{3}{4}}\right) \approx 83.138</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1200\left(\tfrac{\sqrt{3}}{4\phi^2}\right) \approx 198.48</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>1200\left(\tfrac{2\sqrt{3}}{4\phi^2}\right) \approx 396.95</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>720\left(\tfrac{\sqrt{25+10\sqrt{5}}}{8\phi^4}\right) \approx 90.366</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>720\left(\tfrac{\sqrt{25+10\sqrt{5}}}{4\phi^4}\right) \approx 180.73</math>}}}}
|-
!style="vertical-align:top;text-align:right;"|Volume
|{{#ifeq:{{{radius|1}}}|1|<math>5\left(\tfrac{5\sqrt{5}}{24}\right) \approx 2.329</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>5\left(\tfrac{5\sqrt{10}}{12}\right) \approx 6.588</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>16\left(\tfrac{1}{3}\right) \approx 5.333</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>16\left(\tfrac{2\sqrt{2}}{3}\right) \approx 15.085</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>8</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>8\sqrt{8} \approx 22.627</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>24\left(\tfrac{\sqrt{2}}{3}\right) \approx 11.314</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>24\left(\tfrac{4}{3}\right) = 32</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>600\left(\tfrac{\sqrt{2}}{12\phi^3}\right) \approx 16.693</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>600\left(\tfrac{4}{12\phi^3}\right) \approx 47.214</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>120\left(\tfrac{15 + 7\sqrt{5}}{4\phi^6\sqrt{8}}\right) \approx 18.118</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>120\left(\tfrac{15 + 7\sqrt{5}}{4\phi^6}\right) \approx 51.246</math>}}}}
|-
!style="vertical-align:top;text-align:right;"|4-Content
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{\sqrt{5}}{24}\left(\tfrac{\sqrt{5}}{2}\right)^4 \approx 0.146</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\sqrt{5}}{24}\left(\sqrt{5}\right)^4 \approx 2.329</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{2}{3} \approx 0.667</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{8}{3} \approx 2.666</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>1</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>4</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>2</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>8</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{\text{Short}\times\text{Vol}}{4} \approx 3.863</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\text{Short}\times\text{Vol}}{4} \approx 15.451</math>}}}}
|{{#ifeq:{{{radius|1}}}|1|<math>\tfrac{\text{Short}\times\text{Vol}}{4} \approx 4.193</math>|{{#ifeq:{{{radius}}}|{{radic|2}}|<math>\tfrac{\text{Short}\times\text{Vol}}{4} \approx 16.770</math>}}}}
|}<noinclude>
[[Category:Geometry templates]]
</noinclude>

Template:Regular convex 4-polytopes - Revision history

OpenDEM 1: 1 revision imported from :wikipedia:en:Template:Regular_convex_4-polytopes

wikipedia:en>HaToll: Undid revision 1292388333 by HaToll (talk)