In geometry, the great dodecicosacron (or great dipteral trisicosahedron) is the dual of the great dodecicosahedron (U63). It has 60 intersecting bow-tie-shaped faces.
Proportionsedit
Each face has two angles of and two angles of . The diagonals of each antiparallelogram intersect at an angle of . The dihedral angle equals . The ratio between the lengths of the long edges and the short ones equals , which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.
great, dodecicosacron, type, star, polyhedron, face, elements, 120v, symmetry, group, index, references, du63, dual, polyhedron, great, dodecicosahedron, geometry, great, dodecicosacron, great, dipteral, trisicosahedron, dual, great, dodecicosahedron, intersec. Great dodecicosacron Type Star polyhedron Face Elements F 60 E 120V 32 x 28 Symmetry group Ih 5 3 532 Index references DU63 dual polyhedron Great dodecicosahedron In geometry the great dodecicosacron or great dipteral trisicosahedron is the dual of the great dodecicosahedron U63 It has 60 intersecting bow tie shaped faces 3D model of a great dodecicosacronProportions editEach face has two angles of arccos 3 4 1 20 5 30 480 324 565 36 displaystyle arccos frac 3 4 frac 1 20 sqrt 5 approx 30 480 324 565 36 circ nbsp and two angles of arccos 5 12 1 4 5 81 816 127 508 183 displaystyle arccos frac 5 12 frac 1 4 sqrt 5 approx 81 816 127 508 183 circ nbsp The diagonals of each antiparallelogram intersect at an angle of arccos 5 12 1 60 5 67 703 547 926 46 displaystyle arccos frac 5 12 frac 1 60 sqrt 5 approx 67 703 547 926 46 circ nbsp The dihedral angle equals arccos 44 3 5 61 127 686 523 427 48 displaystyle arccos frac 44 3 sqrt 5 61 approx 127 686 523 427 48 circ nbsp The ratio between the lengths of the long edges and the short ones equals 1 2 1 2 5 displaystyle frac 1 2 frac 1 2 sqrt 5 nbsp which is the golden ratio Part of each face lies inside the solid hence is invisible in solid models References editWenninger Magnus 1983 Dual Models Cambridge University Press ISBN 978 0 521 54325 5 MR 0730208External links editWeisstein Eric W Great dodecicosacron MathWorld Uniform polyhedra and duals nbsp This polyhedron related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Great dodecicosacron amp oldid 1129952080, wikipedia, wiki, book, books, library,