Convex Regular Polyhedra with Coplanar Squares and Pentagons
After listing Convex Diamond-Regular Polyhedra there are still a few remaining cases of convex regular polyhedra that contain coplanar squares and pentagons.
There are only seven cases given these constraints. None are chiral.
Including these seven cases, and the 71 Diamond-Regular Polyhedra, this list has been proven to be complete.
Each figure lists the number of faces of each type - Triangle, Square, Pentagon, Hexagon, Octagon and Decagon, as well as the total Face, Edge and Vertex counts, and Symmetry Symbol.
Links below display various models
- Clicking on pictures opens an Interactive OFF Viewer
- OFF files open in an online browser. Downloaded files may be viewed with an application such as Antiprism
- STEL files may be saved and opened with Stella
- VRML files (wrl,switch,cyl) open in an online browser. Downloaded files may be viewed with a VRML browser such as FreeWRL
| Convex Regular Cases with Coplanar Squares and Triangles |
|---|
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| augmented 3+4-prism | | (1)Cube+(1)Triangular Prism+(1)J1 | SYM | 3 | 4 | 5 | 6 | 8 | 10 | | C2v | 6 | 6 | * | * | * | * | | S9 | F=12 E=21 V=11 |  | | off stel wrl switch |
|
|
| 3+4+3-prism,2 | | (1)Cube+(2)Triangular Prism | SYM | 3 | 4 | 5 | 6 | 8 | 10 | | D2h | 6 | 6 | * | * | * | * | | S11 | F=12 E=21 V=11 |  | | off stel wrl switch |
|
| Convex Regular Cases with Coplanar Pentagons and Triangles |
|---|
| 3+5-prism | (1)Pentagonal Prism+
(1)Triangular Prism | SYM | 3 | 4 | 5 | 6 | 8 | 10 | | C2v | 2 | 6 | 2 | * | * | * | | S5 | F=10 E=20 V=12 |  | | off stel wrl switch |
|
| 3+5+3-prism | (1)Pentagonal Prism+
(2)Triangular Prism | SYM | 3 | 4 | 5 | 6 | 8 | 10 | | C2v | 2 | 7 | 2 | * | * | * | | S12 | F=11 E=22 V=13 |  | | off stel wrl switch |
|
| augmented 3+5-prism | (1)Pentagonal Prism+
(1)Triangular Prism+(1)J1 | SYM | 3 | 4 | 5 | 6 | 8 | 10 | | Cs | 6 | 5 | 2 | * | * | * | | S13 | F=13 E=24 V=13 |  | | off stel wrl switch |
|
Question or comments about the web page should be directed to PolyhedraSmith@gmail.com.
Generation of VRML models was expedited by the use of Robert Webb's Stella
application, and the .Stel files are available above to Stella users. The
Hedron application by
Jim McNeill was used extensively for model creation and to generate switch files.
I'd also like to thank
Alex Doskey
for his spreadsheet method which made the construction of this page much
easier. I also use JovoToys
in polyhedra contruction.
History:
2024-06-17 Use base.css
2024-06-13 Switch to Multi OFF Viewer
2023-09-10 Added Timofeenko models and Zalgaller names
2023-09-06 Switch to Simple OFF Viewer and X_Ite VRML Viewer
2023-03-17 Initial Release
Back to the main Polyhedron Page.
Link to this page as http://www.interocitors.com/polyhedra/120s/Extended
