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.
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.