rhombicosidodecahedron

E620946

A rhombicosidodecahedron is a highly symmetric Archimedean solid with 62 faces (20 triangular, 30 square, and 12 pentagonal), 120 edges, and 60 vertices.

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Statements (49)

Predicate Object
instanceOf uniform polyhedron
belongsToFamily Archimedean solids NERFINISHED
hasAlternateName rhombicosidodecahedral polyhedron
small rhombicosidodecahedron
hasCategory polyhedral geometry
three-dimensional geometry
hasCircumradiusFormula (a/2) * sqrt(8 + 2*sqrt(5))
hasConstructionMethod cantellation of the dodecahedron
cantellation of the icosahedron
rectification of the dodecahedron and icosahedron
hasCoxeterDiagram 4 3 5
hasDihedralAngleBetweenSquaresAndPentagons 144 degrees
hasDihedralAngleBetweenSquaresAndTriangles 135 degrees
hasDihedralAngleBetweenTrianglesAndPentagons 150 degrees
hasDiscoveryAttribution Archimedes of Syracuse NERFINISHED
hasDualPolyhedron deltoidal hexecontahedron
hasEdgeCountRelation each edge shared by 2 faces
hasEdgeGraph 4-regular graph with 60 vertices
hasEdgeLengthSymbol a
hasEulerCharacteristic 2
hasFaceCountRelation 20 triangles + 30 squares + 12 pentagons = 62 faces
hasFaceTransitivityCount 3
hasFaceType regular pentagon
square
triangle
hasInradiusToFacesFormula (a/2) * sqrt(5 + 2*sqrt(5))
hasNet multiple distinct nets
hasNumberOfArchimedeanSolidIndex 11
hasNumberOfEdges 120
hasNumberOfFaces 62
hasNumberOfPentagonalFaces 12
hasNumberOfSquareFaces 30
hasNumberOfTriangularFaces 20
hasNumberOfVertices 60
hasSchlafliSymbol rr{5,3}
hasSurfaceAreaFormula A = (30 + 10*sqrt(3) + 12*sqrt(25 + 10*sqrt(5))) * a^2
hasSymmetryGroup Ih
icosahedral symmetry
hasVertexConfiguration 3.4.5.4
hasVertexFigureDescription one triangle, two squares, one pentagon at each vertex
hasVolumeFormula V = (60 + 29*sqrt(5)) * a^3 / 3
hasWythoffSymbol 3 | 5 2
isConvex true
isEdgeTransitive true
isFaceTransitive false
isSpaceFilling false
isUniform true
isVertexTransitive true
isZonohedron true

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Archimedean solids hasElement rhombicosidodecahedron