|
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol . It is also called a C120, hecatonicosachoron, dodecacontachoron and hecatonicosahedroid.〔Matila Ghyka, ''The Geometry of Art and Life'' (1977), p.68〕 The boundary of the 120-cell is composed of 120 dodecahedral cells with 4 meeting at each vertex. It can be thought of as the 4-dimensional analog of the dodecahedron and has been called a dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron. Just as a dodecahedron can be built up as a model with 12 pentagons, 3 around each vertex, the ''dodecaplex'' can be built up from 120 dodecahedra, with 3 around each edge. The Davis 120-cell, introduced by , is a compact 4-dimensional hyperbolic manifold obtained by identifying opposite faces of the 120-cell, whose universal cover gives the regular honeycomb of 4-dimensional hyperbolic space. == Elements == *There are 120 cells, 720 pentagonal faces, 1200 edges, and 600 vertices. *There are 4 dodecahedra, 6 pentagons, and 4 edges meeting at every vertex. *There are 3 dodecahedra and 3 pentagons meeting every edge. *The dual polytope of the 120-cell is the 600-cell. *The vertex figure of the 120-cell is a tetrahedron. *The dihedral angle (angle between facet hyperplanes) of the 120-cell is 144°〔Coxeter, Regular polygons, p.293〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「120-cell」の詳細全文を読む スポンサード リンク
|