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In geometry, a disphenoid (also bisphenoid) (from Greek sphenoeides, "wedgelike" 〔(Merriam-Webster Online Dictionary )''.〕) is a tetrahedron whose four faces are congruent acute-angled triangles.〔 *Coxeter, ''Regular Polytopes'', 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. p. 15〕 It can also be described as a tetrahedron in which every two edges that are opposite each other have equal lengths. Other names are isosceles tetrahedron and equifacial tetrahedron. They can also be seen as digonal antiprisms as an alternated quadrilateral prism. All the solid angles and vertex figures of a disphenoid are the same, and the sum of the face angles at each vertex is equal to two right angles. However, a disphenoid is not a regular polyhedron, because, in general, its faces are not regular polygons, and it is not edge-transitive . == Special cases and generalizations == If the faces of a disphenoid are equilateral triangles, it is a regular tetrahedron with Td tetrahedral symmetry, although this is not normally called a disphenoid. The faces of a tetragonal disphenoid are identical isosceles, and it has D2d dihedral symmetry. The faces of a rhombic disphenoid are scalene and it has D2 dihedral symmetry. Tetragonal disphenoids and rhombic disphenoids are isohedra. The digonal disphenoid is not a disphenoid as defined above. It has two sets of isosceles triangles faces, and it has C2v. The most general disphenoid term is the phyllic disphenoid with only two types of scalene triangles. Tetrahedral diagrams are included for each type below, with edges colored by isometric equivalence, and are gray colored for unique edges. |50px |Identical isosceles triangles |D2d S4||() ()|| ||2 *2 2×||8 4 |- align=center |Rhombic disphenoid |50px |Identical scalene triangles |D2||()+||||222||4 |- align=center |rowspan=2|Digonal disphenoid ∨ |60px |Two equilateral and two isosceles triangles |rowspan=2|C2v C2||rowspan=2|() ()+||rowspan=2| ||rowspan=2| *22 22||rowspan=2|4 2 |- align=center |60px |rowspan=2|Two types of isosceles triangles |-align=center |rowspan=2|Phyllic disphenoid |60px |rowspan=2|C2||rowspan=2|()+||rowspan=2| ||rowspan=2|22 ||rowspan=2|2 |- align=center |60px |Two types of scalene triangles |} 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「Disphenoid」の詳細全文を読む スポンサード リンク
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