❴5,5∣3❵

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{5,5∣3}
Rank3
TypeRegular
Notation
Schläfli symbol{5,5∣3}
Elements
Faces12 pentagons
Edges30
Vertices12
Vertex figurePentagon
Petrie polygons10 hexagons
Holes20 triangles
Related polytopes
Dual{5,5∣3}
φ 2 Icosahedron
Abstract & topological properties
Flag count120
Schläfli type{5,5}
OrientableYes
SkeletonIcosahedral graph

{5,5∣3} is an abstract regular polyhedron. It is a quotient of the order-5 pentagonal tiling with triangular holes. It is a regular tessellation of Bring's surface.

Realizations[edit | edit source]

{5,5∣3} has two faithful symmetric realizations in 3-dimensional space, the great dodecahedron and the small stellated dodecahedron. There are in total 6 faithful symmetric realizations of {5,5∣3}. The great dodecahedron and the small stellated dodecahedron are the only pure faithfully symmetric realizations, the others are the results of blending those two along with {5,5∣3}/2.

Faithful symmetric realizations of {5,5∣3}
Dimension Components Name
3 Great dodecahedron Great dodecahedron
3 Small stellated dodecahedron Small stellated dodecahedron
6
8
8
11

External links[edit | edit source]