Basix | basix.ElementFamily.P ↓ Show Basix examples ↓↑ Hide Basix examples ↑Before running this example, you must install Basix: pip3 install fenics-basix This element can then be created with the following lines of Python: import basix
# Create discontinuous Lagrange (equispaced variant) degree 0 on a interval element = basix.create_element(basix.ElementFamily.P, basix.CellType.interval, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a interval element = basix.create_element(basix.ElementFamily.P, basix.CellType.interval, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a interval element = basix.create_element(basix.ElementFamily.P, basix.CellType.interval, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a triangle element = basix.create_element(basix.ElementFamily.P, basix.CellType.triangle, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a triangle element = basix.create_element(basix.ElementFamily.P, basix.CellType.triangle, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a triangle element = basix.create_element(basix.ElementFamily.P, basix.CellType.triangle, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a quadrilateral element = basix.create_element(basix.ElementFamily.P, basix.CellType.quadrilateral, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a quadrilateral element = basix.create_element(basix.ElementFamily.P, basix.CellType.quadrilateral, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a quadrilateral element = basix.create_element(basix.ElementFamily.P, basix.CellType.quadrilateral, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a tetrahedron element = basix.create_element(basix.ElementFamily.P, basix.CellType.tetrahedron, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a tetrahedron element = basix.create_element(basix.ElementFamily.P, basix.CellType.tetrahedron, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a tetrahedron element = basix.create_element(basix.ElementFamily.P, basix.CellType.tetrahedron, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a hexahedron element = basix.create_element(basix.ElementFamily.P, basix.CellType.hexahedron, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a hexahedron element = basix.create_element(basix.ElementFamily.P, basix.CellType.hexahedron, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a hexahedron element = basix.create_element(basix.ElementFamily.P, basix.CellType.hexahedron, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a prism element = basix.create_element(basix.ElementFamily.P, basix.CellType.prism, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a prism element = basix.create_element(basix.ElementFamily.P, basix.CellType.prism, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a prism element = basix.create_element(basix.ElementFamily.P, basix.CellType.prism, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True) This implementation is correct for all the examples below that it supports. Correct: interval,0,equispaced; interval,1,equispaced; interval,2,equispaced; triangle,0,equispaced; triangle,1,equispaced; triangle,2,equispaced; quadrilateral,0,equispaced; quadrilateral,1,equispaced; quadrilateral,2,equispaced; tetrahedron,0,equispaced; tetrahedron,1,equispaced; tetrahedron,2,equispaced; hexahedron,0,equispaced; hexahedron,1,equispaced; hexahedron,2,equispaced; prism,0,equispaced; prism,1,equispaced; prism,2,equispaced Not implemented: pyramid,0,equispaced; pyramid,1,equispaced; pyramid,2,equispaced |
Basix.UFL | basix.ElementFamily.P ↓ Show Basix.UFL examples ↓↑ Hide Basix.UFL examples ↑Before running this example, you must install Basix.UFL: pip3 install fenics-basix fenics-ufl This element can then be created with the following lines of Python: import basix import basix.ufl
# Create discontinuous Lagrange (equispaced variant) degree 0 on a interval element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.interval, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a interval element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.interval, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a interval element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.interval, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a triangle element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.triangle, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a triangle element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.triangle, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a triangle element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.triangle, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a quadrilateral element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.quadrilateral, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a quadrilateral element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.quadrilateral, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a quadrilateral element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.quadrilateral, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a tetrahedron element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.tetrahedron, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a tetrahedron element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.tetrahedron, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a tetrahedron element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.tetrahedron, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a hexahedron element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.hexahedron, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a hexahedron element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.hexahedron, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a hexahedron element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.hexahedron, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a prism element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.prism, 0, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a prism element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.prism, 1, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a prism element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.prism, 2, lagrange_variant=basix.LagrangeVariant.equispaced, discontinuous=True) This implementation is correct for all the examples below that it supports. Correct: interval,0,equispaced; interval,1,equispaced; interval,2,equispaced; triangle,0,equispaced; triangle,1,equispaced; triangle,2,equispaced; quadrilateral,0,equispaced; quadrilateral,1,equispaced; quadrilateral,2,equispaced; tetrahedron,0,equispaced; tetrahedron,1,equispaced; tetrahedron,2,equispaced; hexahedron,0,equispaced; hexahedron,1,equispaced; hexahedron,2,equispaced; prism,0,equispaced; prism,1,equispaced; prism,2,equispaced Not implemented: pyramid,0,equispaced; pyramid,1,equispaced; pyramid,2,equispaced |
Bempp-cl | "DP" ↓ Show Bempp-cl examples ↓↑ Hide Bempp-cl examples ↑Before running this example, you must install Bempp-cl: pip3 install numba scipy meshio pip3 install bempp-cl This element can then be created with the following lines of Python: import bempp_cl.api grid = bempp_cl.api.shapes.regular_sphere(1)
# Create discontinuous Lagrange degree 0 element = bempp_cl.api.function_space(grid, "DP", 0)
# Create discontinuous Lagrange degree 1 element = bempp_cl.api.function_space(grid, "DP", 1) |
FIAT | FIAT.DiscontinuousLagrange ↓ Show FIAT examples ↓↑ Hide FIAT examples ↑Before running this example, you must install FIAT: pip3 install git+https://github.com/firedrakeproject/fiat.git This element can then be created with the following lines of Python: import FIAT
# Create discontinuous Lagrange (equispaced variant) degree 0 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("interval"), 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("interval"), 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("interval"), 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("triangle"), 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("triangle"), 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("triangle"), 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("tetrahedron"), 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("tetrahedron"), 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 element = FIAT.DiscontinuousLagrange(FIAT.ufc_cell("tetrahedron"), 2) This implementation is correct for all the examples below that it supports. Correct: interval,0,equispaced; interval,1,equispaced; interval,2,equispaced; triangle,0,equispaced; triangle,1,equispaced; triangle,2,equispaced; tetrahedron,0,equispaced; tetrahedron,1,equispaced; tetrahedron,2,equispaced Not implemented: quadrilateral,0,equispaced; quadrilateral,1,equispaced; quadrilateral,2,equispaced; hexahedron,0,equispaced; hexahedron,1,equispaced; hexahedron,2,equispaced; prism,0,equispaced; prism,1,equispaced; prism,2,equispaced; pyramid,0,equispaced; pyramid,1,equispaced; pyramid,2,equispaced |
NDElement | Family.Lagrange, continuity=Continuity.Discontinuous ↓ Show NDElement examples ↓↑ Hide NDElement examples ↑Before running this example, you must install NDElement: pip3 install ndelement This element can then be created with the following lines of Python: from ndelement.ciarlet import Continuity, Family, create_family from ndelement.reference_cell import ReferenceCellType
# Create discontinuous Lagrange (equispaced variant) degree 0 on a interval family = create_family(Family.Lagrange, 0, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Interval)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a interval family = create_family(Family.Lagrange, 1, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Interval)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a interval family = create_family(Family.Lagrange, 2, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Interval)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a triangle family = create_family(Family.Lagrange, 0, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Triangle)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a triangle family = create_family(Family.Lagrange, 1, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Triangle)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a triangle family = create_family(Family.Lagrange, 2, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Triangle)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a quadrilateral family = create_family(Family.Lagrange, 0, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Quadrilateral)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a quadrilateral family = create_family(Family.Lagrange, 1, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Quadrilateral)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a quadrilateral family = create_family(Family.Lagrange, 2, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Quadrilateral)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a tetrahedron family = create_family(Family.Lagrange, 0, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Tetrahedron)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a tetrahedron family = create_family(Family.Lagrange, 1, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Tetrahedron)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a tetrahedron family = create_family(Family.Lagrange, 2, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Tetrahedron)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a hexahedron family = create_family(Family.Lagrange, 0, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Hexahedron)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a hexahedron family = create_family(Family.Lagrange, 1, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Hexahedron)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a hexahedron family = create_family(Family.Lagrange, 2, continuity=Continuity.Discontinuous) element = family.element(ReferenceCellType.Hexahedron) This implementation is correct for all the examples below that it supports. Correct: interval,0,equispaced; interval,1,equispaced; interval,2,equispaced; triangle,0,equispaced; triangle,1,equispaced; triangle,2,equispaced; quadrilateral,0,equispaced; quadrilateral,1,equispaced; quadrilateral,2,equispaced; tetrahedron,0,equispaced; tetrahedron,1,equispaced; tetrahedron,2,equispaced; hexahedron,0,equispaced; hexahedron,1,equispaced; hexahedron,2,equispaced Not implemented: prism,0,equispaced; prism,1,equispaced; prism,2,equispaced; pyramid,0,equispaced; pyramid,1,equispaced; pyramid,2,equispaced |
Symfem | "discontinuous Lagrange" (equispaced)
"discontinuous Lagrange", variant="gll" (interval, GLL)
"discontinuous Q", variant="gll" (quadrilateral, GLL; hexahedron, GLL)
"discontinuous Lagrange", variant="gl" (interval, GL)
"discontinuous Q", variant="gl" (quadrilateral, GL; hexahedron, GL)
"discontinuous Lagrange", variant="legendre" (Legendre) ↓ Show Symfem examples ↓↑ Hide Symfem examples ↑Before running this example, you must install Symfem: pip3 install symfem This element can then be created with the following lines of Python: import symfem
# Create discontinuous Lagrange (equispaced variant) degree 0 on a interval element = symfem.create_element("interval", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a interval element = symfem.create_element("interval", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a interval element = symfem.create_element("interval", "discontinuous Lagrange", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a triangle element = symfem.create_element("triangle", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a triangle element = symfem.create_element("triangle", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a triangle element = symfem.create_element("triangle", "discontinuous Lagrange", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a quadrilateral element = symfem.create_element("quadrilateral", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a quadrilateral element = symfem.create_element("quadrilateral", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a quadrilateral element = symfem.create_element("quadrilateral", "discontinuous Lagrange", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a tetrahedron element = symfem.create_element("tetrahedron", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a tetrahedron element = symfem.create_element("tetrahedron", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a tetrahedron element = symfem.create_element("tetrahedron", "discontinuous Lagrange", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a hexahedron element = symfem.create_element("hexahedron", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a hexahedron element = symfem.create_element("hexahedron", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a hexahedron element = symfem.create_element("hexahedron", "discontinuous Lagrange", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a prism element = symfem.create_element("prism", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a prism element = symfem.create_element("prism", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a prism element = symfem.create_element("prism", "discontinuous Lagrange", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a pyramid element = symfem.create_element("pyramid", "discontinuous Lagrange", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a pyramid element = symfem.create_element("pyramid", "discontinuous Lagrange", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a pyramid element = symfem.create_element("pyramid", "discontinuous Lagrange", 2) This implementation is used to compute the examples below and verify other implementations. |
(legacy) UFL | "Discontinuous Lagrange" (interval, equispaced; triangle, equispaced; tetrahedron, equispaced)
"DQ" (quadrilateral, equispaced; hexahedron, equispaced) ↓ Show (legacy) UFL examples ↓↑ Hide (legacy) UFL examples ↑Before running this example, you must install (legacy) UFL: pip3 install setuptools pip3 install fenics-ufl-legacy This element can then be created with the following lines of Python: import ufl_legacy
# Create discontinuous Lagrange (equispaced variant) degree 0 on a interval element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "interval", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a interval element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "interval", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a interval element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "interval", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a triangle element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "triangle", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a triangle element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "triangle", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a triangle element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "triangle", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a quadrilateral element = ufl_legacy.FiniteElement("DQ", "quadrilateral", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a quadrilateral element = ufl_legacy.FiniteElement("DQ", "quadrilateral", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a quadrilateral element = ufl_legacy.FiniteElement("DQ", "quadrilateral", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a tetrahedron element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "tetrahedron", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a tetrahedron element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "tetrahedron", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a tetrahedron element = ufl_legacy.FiniteElement("Discontinuous Lagrange", "tetrahedron", 2)
# Create discontinuous Lagrange (equispaced variant) degree 0 on a hexahedron element = ufl_legacy.FiniteElement("DQ", "hexahedron", 0)
# Create discontinuous Lagrange (equispaced variant) degree 1 on a hexahedron element = ufl_legacy.FiniteElement("DQ", "hexahedron", 1)
# Create discontinuous Lagrange (equispaced variant) degree 2 on a hexahedron element = ufl_legacy.FiniteElement("DQ", "hexahedron", 2) |