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In geometry, demihypercubes (also called ''n-demicubes'', ''n-hemicubes'', and ''half measure polytopes'') are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as ''hγn'' for being ''half'' of the hypercube family, ''γn''. Half of the vertices are deleted and new facets are formed. The ''2n'' facets become ''2n'' (n-1)-demicubes, and 2n (n-1)-simplex facets are formed in place of the deleted vertices.〔Regular and semi-regular polytopes III, p. 315-316〕 They have been named with a ''demi-'' prefix to each hypercube name: demicube, demitesseract, etc. The demicube is identical to the regular tetrahedron, and the demitesseract is identical to the regular 16-cell. The demipenteract is considered ''semiregular'' for having only regular facets. Higher forms don't have all regular facets but are all uniform polytopes. The vertices and edges of a demihypercube form two copies of the halved cube graph. == Discovery == Thorold Gosset described the demipenteract in his 1900 publication listing all of the regular and semiregular figures in n-dimensions above 3. He called it a ''5-ic semi-regular''. It also exists within the semiregular k21 polytope family. The demihypercubes can be represented by extended Schläfli symbols of the form h as half the vertices of . The vertex figures of demihypercubes are rectified n-simplexes. 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「Demihypercube」の詳細全文を読む スポンサード リンク
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