Pentahedron

Author

Eric W. Weisstein
June 17, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/Pentahedron.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Pentahedron.html.

©2023 Wolfram Research, Inc. except for portions noted otherwise

Examples

FirstCase[Import["https://oeis.org/A000944/b000944.txt","Table"],{5,n_}:>n]

GraphData["Polyhedral",5]

Length[%]

TextGrid[Sort[PolyhedronData[#,{"F","V","E","#"}]&/@PolyhedronData[5]],Dividers->All,Alignment->{{{Decimal},Left}}]

Enumeration

V6

PolyhedronName/@(polys=Sort[Select[Join[Platonics,Archimedeans,JohnsonSolids,First/@ArchimedeanDuals,{Prism[3]}],(Length[PolyhedronFaces[#]]==5&)],OrderedQ[PolyhedronName@@{##}]&])//ColumnForm

Show[GraphicsArray[Partition[Graphics3D[Polyhedron[#],PlotLabel->StyleForm[StringJoin@@StringSplit[PolyhedronName[#]," "->"\n"],FontFamily->"Times",TextAlignment->0,FontSlant->"Italic"],Boxed->False]&/@polys,2]],ImageSize->400,GraphicsSpacing->{-.2,0}]

Show[GraphicsArray[
{
Graphics[HiddenWireframe[#,PlotStyles->{{},Dashing[{1,1}.04]}],AspectRatio->Automatic]&/@{Pyramid[4],Prism[3]},
ShowGraph[#,AspectRatio->Automatic,DisplayFunction->Identity,
VertexStyle->Disk[.07],
VertexColor->Red]&/@Polyhedra[5],
ShowGraph[#,AspectRatio->Automatic,DisplayFunction->Identity,
VertexStyle->Disk[.07],
VertexColor->Red]&/@PolyhedralGraphs[5]
}
]]

V6

GraphicsGrid[{Show[PolyhedronData[#],PlotLabel->PolyhedronData[#,"Name"],Boxed->False,BaseStyle->Italic]&/@PolyhedronData[5]}]