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In geometry, a Goursat tetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane on 3-dimensional surfaces: the 3-sphere, the Euclidean 3-space, and hyperbolic 3-space. Coxeter named them after Édouard Goursat who first looked into these domains. It is an extension of the theory of Schwarz triangles for Wythoff constructions on the sphere. ==Graphical representation== A Goursat tetrahedron can be represented graphically by a tetrahedral graph, which is in a dual configuration of the fundamental domain tetrahedron. In the graph, each node represents a face (mirror) of the Goursat tetrahedron. Each edge is labeled by a rational value corresponding to the reflection order, being π/dihedral angle. :100px A 4-node Coxeter-Dynkin diagram represents this tetrahedral graphs with order-2 edges hidden. If many edges are order 2, the Coxeter group can be represented by a bracket notation. Existence requires each of the 3-node subgraphs of this graph, (p q r), (p u s), (q t u), and (r s t), must correspond to a Schwarz triangle. 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「Goursat tetrahedron」の詳細全文を読む スポンサード リンク
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