|
In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes. E.L. Elte compiled a longer list in 1912 as ''The Semiregular Polytopes of the Hyperspaces'' which included a wider definition. == Gosset's list == In three-dimensional space and below, the terms ''semiregular polytope'' and ''uniform polytope'' have identical meanings, because all uniform polygons must be regular. However, since not all uniform polyhedra are regular, the number of semiregular polytopes in dimensions higher than three is much smaller than the number of uniform polytopes in the same number of dimensions. The three convex semiregular 4-polytopes are the rectified 5-cell, snub 24-cell and rectified 600-cell. The only semiregular polytopes in higher dimensions are the ''k''21 polytopes, where the rectified 5-cell is the special case of ''k'' = 0. These were all listed by Gosset, but a proof of the completeness of this list was not published until the work of for four dimensions, and for higher dimensions. ;Gosset's 4-polytopes (with his names in parentheses): :Rectified 5-cell (Tetroctahedric), :Rectified 600-cell (Octicosahedric), :Snub 24-cell (Tetricosahedric), ;Semiregular E-polytopes in higher dimensions: :5-demicube (5-ic semi-regular), a 5-polytope, ↔ :221 polytope (6-ic semi-regular), a 6-polytope, :321 polytope (7-ic semi-regular), a 7-polytope, :421 polytope (8-ic semi-regular), an 8-polytope, 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「semiregular polytope」の詳細全文を読む スポンサード リンク
|