Sphenocorona: Difference between revisions
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under the action of the group generated by reflections about the xz-plane and the yz-plane.<ref>{{Cite journal|last=Timofeenko|first=A. V.|date=2009|title=The non-Platonic and non-Archimedean noncomposite polyhedra|url=|journal=Journal of Mathematical Science|volume=162|issue=5|pages=718}}</ref> |
under the action of the group generated by reflections about the xz-plane and the yz-plane.<ref>{{Cite journal|last=Timofeenko|first=A. V.|date=2009|title=The non-Platonic and non-Archimedean noncomposite polyhedra|url=|journal=Journal of Mathematical Science|volume=162|issue=5|pages=718}}</ref> |
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We may then calculate the [[surface area]] of a |
We may then calculate the [[surface area]] of a sphenocorona of edge length ''a'' as |
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: <math>A=(2+3\sqrt{3})a^2,</math><ref>{{Cite journal|last=Wolfram Research, Inc.|first=|date=2020|title=Wolfram{{!}}Alpha Knowledgebase|url=|journal=|location=Champaign, IL|volume=|pages=|quote=<code>PolyhedronData[{"Johnson", 86},"SurfaceArea"]</code>|via=}}</ref> |
: <math>A=(2+3\sqrt{3})a^2,</math><ref>{{Cite journal|last=Wolfram Research, Inc.|first=|date=2020|title=Wolfram{{!}}Alpha Knowledgebase|url=|journal=|location=Champaign, IL|volume=|pages=|quote=<code>PolyhedronData[{"Johnson", 86},"SurfaceArea"]</code>|via=}}</ref> |
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Revision as of 04:47, 12 April 2020
| Sphenocorona | |
|---|---|
 | |
| Type | Johnson J85 - J86 - J87 |
| Faces | 2x2+2x4 triangles 2 squares |
| Edges | 22 |
| Vertices | 10 |
| Vertex configuration | 4(33.4) 2(32.42) 2x2(35) |
| Symmetry group | C2v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the sphenocorona is one of the Johnson solids (J86).
A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]
The sphenocorona is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.
Cartesian coordinates
Let k ≈ 0.85273 be the smallest positive root of the quartic polynomial
Then, Cartesian coordinates of a sphenocorona with edge length 2 are given by the union of the orbits of the points
under the action of the group generated by reflections about the xz-plane and the yz-plane.[2]
We may then calculate the surface area of a sphenocorona of edge length a as
and its volume as
See also
References
- ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.
- ^ Timofeenko, A. V. (2009). "The non-Platonic and non-Archimedean noncomposite polyhedra". Journal of Mathematical Science. 162 (5): 718.
- ^ Wolfram Research, Inc. (2020). "Wolfram|Alpha Knowledgebase". Champaign, IL.
PolyhedronData[{"Johnson", 86},"SurfaceArea"]{{cite journal}}: Cite journal requires|journal=(help) - ^ Wolfram Research, Inc. (2020). "Wolfram|Alpha Knowledgebase". Champaign, IL.
PolyhedronData[{"Johnson", 86},"Volume"]{{cite journal}}: Cite journal requires|journal=(help)
External links
- Weisstein, Eric W., "Sphenocorona" ("Johnson solid") at MathWorld.
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