| dbo:abstract
|
- In geometry, the Hessian polyhedron is a regular complex polyhedron 3{3}3{3}3, , in . It has 27 vertices, 72 3{} edges, and 27 3{3}3 faces. It is self-dual. Coxeter named it after Ludwig Otto Hesse for sharing the Hessian configuration or (94123), 9 points lying by threes on twelve lines, with four lines through each point. Its complex reflection group is 3[3]3[3]3 or , order 648, also called a Hessian group. It has 27 copies of , order 24, at each vertex. It has 24 order-3 reflections. Its Coxeter number is 12, with degrees of the fundamental invariants 3, 6, and 12, which can be seen in projective symmetry of the polytopes. The Witting polytope, 3{3}3{3}3{3}3, contains the Hessian polyhedron as cells and vertex figures. It has a real representation as the 221 polytope, , in 6-dimensional space, sharing the same 27 vertices. The 216 edges in 221 can be seen as the 72 3{} edges represented as 3 simple edges. (en)
- 在幾何學中，黑塞二十七面體（Hessian polyhedron）是一個複正多面體，其位於複希爾伯特空間中由27個莫比烏斯－坎特八邊形組成，共有27個面、72條三元邊和27個頂點，是一個自身對偶的多面體，其可以視為實數空間的四面體在複數空間中的類比。 由於這種形狀與黑塞排佈共享結構，即12條線上有9個點，每條線上有3個點，每個點上有4條線，因此考克斯特將這種形狀以路德维希·奥托·黑塞的名字命名。 黑塞二十七面體是一種位於複數空間的立體，其對應到實數空間同樣也有一種實數空間的代表，其為，考克斯特表示法計為，其在六維空間中與黑塞二十七面體共用其27個頂點，其216條邊可透過將三元邊3{}替換成3條簡單邊即可於221中被觀察到。 (zh)
|
| rdfs:comment
|
- 在幾何學中，黑塞二十七面體（Hessian polyhedron）是一個複正多面體，其位於複希爾伯特空間中由27個莫比烏斯－坎特八邊形組成，共有27個面、72條三元邊和27個頂點，是一個自身對偶的多面體，其可以視為實數空間的四面體在複數空間中的類比。 由於這種形狀與黑塞排佈共享結構，即12條線上有9個點，每條線上有3個點，每個點上有4條線，因此考克斯特將這種形狀以路德维希·奥托·黑塞的名字命名。 黑塞二十七面體是一種位於複數空間的立體，其對應到實數空間同樣也有一種實數空間的代表，其為，考克斯特表示法計為，其在六維空間中與黑塞二十七面體共用其27個頂點，其216條邊可透過將三元邊3{}替換成3條簡單邊即可於221中被觀察到。 (zh)
- In geometry, the Hessian polyhedron is a regular complex polyhedron 3{3}3{3}3, , in . It has 27 vertices, 72 3{} edges, and 27 3{3}3 faces. It is self-dual. Coxeter named it after Ludwig Otto Hesse for sharing the Hessian configuration or (94123), 9 points lying by threes on twelve lines, with four lines through each point. The Witting polytope, 3{3}3{3}3{3}3, contains the Hessian polyhedron as cells and vertex figures. (en)
|
