$$\mathsf{P}_{\mathsf{2}}$$
$$\Pm{2}{0}{2}$$
$$\dof{3}{1}{0}{0}{1} \pl \dof{3}{0}{1}{1}{1} = 6$$
("P", triangle, 2)
("P-", triangle, 2, 0)
$$\mathsf{N1}^{\mathsf{e}}_{\mathsf{1}}$$
$$\Pm{1}{1}{3}$$
$$\dof{6}{0}{0}{1}{1} = 6$$
("N1E", tetrahedron, 1)
("P-", tetrahedron, 1, 1)
$$\mathsf{dP}_{\mathsf{2}}$$
$$\Pm{3}{1}{1}$$
$$\dof{1}{2}{0}{1}{3} = 3$$
("DP", interval, 2)
("P-", interval, 3, 1)
$$\mathsf{N1}^{\mathsf{e}}_{\mathsf{2}}$$
$$\Pm{2}{1}{3}$$
$$\dof{6}{1}{0}{1}{2} \pl \dof{4}{0}{1}{2}{2} = 20$$
("N1E", tetrahedron, 2)
("P-", tetrahedron, 2, 1)
$$\mathsf{dP}_{\mathsf{1}}$$
$$\Pm{2}{2}{2}$$
$$\dof{1}{1}{0}{2}{3} = 3$$
("DP", triangle, 1)
("P-", triangle, 2, 2)
$$\Pm{3}{2}{2}$$
$$\dof{1}{2}{0}{2}{6} = 6$$
("DP", triangle, 2)
("P-", triangle, 3, 2)
$$\mathsf{P}_{\mathsf{1}}$$
$$\Pm{1}{0}{1}$$
$$\dof{2}{0}{0}{0}{1} = 2$$
("P", interval, 1)
("P-", interval, 1, 0)
$$\Pm{2}{1}{1}$$
$$\dof{1}{1}{0}{1}{2} = 2$$
("DP", interval, 1)
("P-", interval, 2, 1)
$$\mathsf{RT}^{\mathsf{[e/f]}}_{\mathsf{3}}$$
$$\Pm{3}{1}{2}$$
$$\dof{3}{2}{0}{1}{3} \pl \dof{1}{1}{1}{2}{6} = 15$$
("RT[E,F]", triangle, 3)
("P-", triangle, 3, 1)
$$\Pm{1}{0}{2}$$
$$\dof{3}{0}{0}{0}{1} = 3$$
("P", triangle, 1)
("P-", triangle, 1, 0)
$$\mathsf{P}_{\mathsf{3}}$$
$$\Pm{3}{0}{3}$$
$$\dof{4}{2}{0}{0}{1} \pl \dof{6}{1}{1}{1}{2} \pl \dof{4}{0}{2}{2}{1} = 20$$
("P", tetrahedron, 3)
("P-", tetrahedron, 3, 0)
$$\Pm{3}{0}{1}$$
$$\dof{2}{2}{0}{0}{1} \pl \dof{1}{1}{1}{1}{2} = 4$$
("P", interval, 3)
("P-", interval, 3, 0)
$$\mathsf{N1}^{\mathsf{f}}_{\mathsf{3}}$$
$$\Pm{3}{2}{3}$$
$$\dof{4}{2}{0}{2}{6} \pl \dof{1}{1}{1}{3}{12} = 36$$
("N1F", tetrahedron, 3)
("P-", tetrahedron, 3, 2)
$$\Pm{3}{3}{3}$$
$$\dof{1}{2}{0}{3}{10} = 10$$
("DP", tetrahedron, 2)
("P-", tetrahedron, 3, 3)
$$\mathsf{dP}_{\mathsf{0}}$$
$$\Pm{1}{2}{2}$$
$$\dof{1}{0}{0}{2}{1} = 1$$
("DP", triangle, 0)
("P-", triangle, 1, 2)
$$\Pm{2}{0}{3}$$
$$\dof{4}{1}{0}{0}{1} \pl \dof{6}{0}{1}{1}{1} = 10$$
("P", tetrahedron, 2)
("P-", tetrahedron, 2, 0)
$$\mathsf{N1}^{\mathsf{e}}_{\mathsf{3}}$$
$$\Pm{3}{1}{3}$$
$$\dof{6}{2}{0}{1}{3} \pl \dof{4}{1}{1}{2}{6} \pl \dof{1}{0}{2}{3}{3} = 45$$
("N1E", tetrahedron, 3)
("P-", tetrahedron, 3, 1)
$$\Pm{3}{0}{2}$$
$$\dof{3}{2}{0}{0}{1} \pl \dof{3}{1}{1}{1}{2} \pl \dof{1}{0}{2}{2}{1} = 10$$
("P", triangle, 3)
("P-", triangle, 3, 0)
$$\Pm{1}{3}{3}$$
$$\dof{1}{0}{0}{3}{1} = 1$$
("DP", tetrahedron, 0)
("P-", tetrahedron, 1, 3)
$$\mathsf{RT}^{\mathsf{[e/f]}}_{\mathsf{2}}$$
$$\Pm{2}{1}{2}$$
$$\dof{3}{1}{0}{1}{2} \pl \dof{1}{0}{1}{2}{2} = 8$$
("RT[E,F]", triangle, 2)
("P-", triangle, 2, 1)
$$\mathsf{N1}^{\mathsf{f}}_{\mathsf{1}}$$
$$\Pm{1}{2}{3}$$
$$\dof{4}{0}{0}{2}{1} = 4$$
("N1F", tetrahedron, 1)
("P-", tetrahedron, 1, 2)
$$\Pm{2}{3}{3}$$
$$\dof{1}{1}{0}{3}{4} = 4$$
("DP", tetrahedron, 1)
("P-", tetrahedron, 2, 3)
$$\Pm{1}{1}{1}$$
$$\dof{1}{0}{0}{1}{1} = 1$$
("DP", interval, 0)
("P-", interval, 1, 1)
$$\mathsf{RT}^{\mathsf{[e/f]}}_{\mathsf{1}}$$
$$\Pm{1}{1}{2}$$
$$\dof{3}{0}{0}{1}{1} = 3$$
("RT[E,F]", triangle, 1)
("P-", triangle, 1, 1)
$$\Pm{2}{0}{1}$$
$$\dof{2}{1}{0}{0}{1} \pl \dof{1}{0}{1}{1}{1} = 3$$
("P", interval, 2)
("P-", interval, 2, 0)
$$\Pm{1}{0}{3}$$
$$\dof{4}{0}{0}{0}{1} = 4$$
("P", tetrahedron, 1)
("P-", tetrahedron, 1, 0)
$$\mathsf{N1}^{\mathsf{f}}_{\mathsf{2}}$$
$$\Pm{2}{2}{3}$$
$$\dof{4}{1}{0}{2}{3} \pl \dof{1}{0}{1}{3}{3} = 15$$
("N1F", tetrahedron, 2)
("P-", tetrahedron, 2, 2)
$$\P{2}{0}{2}$$
$$\dofm{3}{2}{0}{0}{1} \pl \dofm{3}{1}{1}{1}{1} = 6$$
("P", triangle, 2, 0)
$$\mathsf{N2}^{\mathsf{f}}_{\mathsf{1}}$$
$$\P{1}{2}{3}$$
$$\dofm{4}{1}{0}{2}{3} = 12$$
("N2F", tetrahedron, 1)
("P", tetrahedron, 1, 2)
$$\P{2}{1}{1}$$
$$\dofm{1}{2}{0}{1}{3} = 3$$
("P", interval, 2, 1)
$$\P{1}{2}{2}$$
$$\dofm{1}{1}{0}{2}{3} = 3$$
("P", triangle, 1, 2)
$$\P{2}{2}{2}$$
$$\dofm{1}{2}{0}{2}{6} = 6$$
("P", triangle, 2, 2)
$$\P{1}{0}{1}$$
$$\dofm{2}{1}{0}{0}{1} = 2$$
("P", interval, 1, 0)
$$\mathsf{N2}^{\mathsf{f}}_{\mathsf{2}}$$
$$\P{2}{2}{3}$$
$$\dofm{4}{2}{0}{2}{6} \pl \dofm{1}{1}{1}{3}{6} = 30$$
("N2F", tetrahedron, 2)
("P", tetrahedron, 2, 2)
$$\P{1}{1}{1}$$
$$\dofm{1}{1}{0}{1}{2} = 2$$
("P", interval, 1, 1)
$$\P{1}{0}{2}$$
$$\dofm{3}{1}{0}{0}{1} = 3$$
("P", triangle, 1, 0)
$$\P{3}{0}{3}$$
$$\dofm{4}{3}{0}{0}{1} \pl \dofm{6}{2}{1}{1}{2} \pl \dofm{4}{1}{2}{2}{1} = 20$$
("P", tetrahedron, 3, 0)
$$\P{3}{0}{1}$$
$$\dofm{2}{3}{0}{0}{1} \pl \dofm{1}{2}{1}{1}{2} = 4$$
("P", interval, 3, 0)
$$\P{2}{3}{3}$$
$$\dofm{1}{2}{0}{3}{10} = 10$$
("P", tetrahedron, 2, 3)
$$\mathsf{dP}_{\mathsf{3}}$$
$$\P{3}{3}{3}$$
$$\dofm{1}{3}{0}{3}{20} = 20$$
("DP", tetrahedron, 3)
("P", tetrahedron, 3, 3)
$$\P{2}{0}{3}$$
$$\dofm{4}{2}{0}{0}{1} \pl \dofm{6}{1}{1}{1}{1} = 10$$
("P", tetrahedron, 2, 0)
$$\P{3}{0}{2}$$
$$\dofm{3}{3}{0}{0}{1} \pl \dofm{3}{2}{1}{1}{2} \pl \dofm{1}{1}{2}{2}{1} = 10$$
("P", triangle, 3, 0)
$$\P{3}{2}{2}$$
$$\dofm{1}{3}{0}{2}{10} = 10$$
("DP", triangle, 3)
("P", triangle, 3, 2)
$$\mathsf{N2}^{\mathsf{e}}_{\mathsf{1}}$$
$$\P{1}{1}{3}$$
$$\dofm{6}{1}{0}{1}{2} = 12$$
("N2E", tetrahedron, 1)
("P", tetrahedron, 1, 1)
$$\P{1}{3}{3}$$
$$\dofm{1}{1}{0}{3}{4} = 4$$
("P", tetrahedron, 1, 3)
$$\mathsf{BDM}^{\mathsf{[e/f]}}_{\mathsf{3}}$$
$$\P{3}{1}{2}$$
$$\dofm{3}{3}{0}{1}{4} \pl \dofm{1}{2}{1}{2}{8} = 20$$
("BDM[E,F]", triangle, 3)
("P", triangle, 3, 1)
$$\mathsf{BDM}^{\mathsf{[e/f]}}_{\mathsf{1}}$$
$$\P{1}{1}{2}$$
$$\dofm{3}{1}{0}{1}{2} = 6$$
("BDM[E,F]", triangle, 1)
("P", triangle, 1, 1)
$$\mathsf{BDM}^{\mathsf{[e/f]}}_{\mathsf{2}}$$
$$\P{2}{1}{2}$$
$$\dofm{3}{2}{0}{1}{3} \pl \dofm{1}{1}{1}{2}{3} = 12$$
("BDM[E,F]", triangle, 2)
("P", triangle, 2, 1)
$$\mathsf{N2}^{\mathsf{f}}_{\mathsf{3}}$$
$$\P{3}{2}{3}$$
$$\dofm{4}{3}{0}{2}{10} \pl \dofm{1}{2}{1}{3}{20} = 60$$
("N2F", tetrahedron, 3)
("P", tetrahedron, 3, 2)
$$\P{2}{0}{1}$$
$$\dofm{2}{2}{0}{0}{1} \pl \dofm{1}{1}{1}{1}{1} = 3$$
("P", interval, 2, 0)
$$\mathsf{N2}^{\mathsf{e}}_{\mathsf{2}}$$
$$\P{2}{1}{3}$$
$$\dofm{6}{2}{0}{1}{3} \pl \dofm{4}{1}{1}{2}{3} = 30$$
("N2E", tetrahedron, 2)
("P", tetrahedron, 2, 1)
$$\P{1}{0}{3}$$
$$\dofm{4}{1}{0}{0}{1} = 4$$
("P", tetrahedron, 1, 0)
$$\mathsf{N2}^{\mathsf{e}}_{\mathsf{3}}$$
$$\P{3}{1}{3}$$
$$\dofm{6}{3}{0}{1}{4} \pl \dofm{4}{2}{1}{2}{8} \pl \dofm{1}{1}{2}{3}{4} = 60$$
("N2E", tetrahedron, 3)
("P", tetrahedron, 3, 1)
$$\P{3}{1}{1}$$
$$\dofm{1}{3}{0}{1}{4} = 4$$
("DP", interval, 3)
("P", interval, 3, 1)
$$\mathsf{Q}_{\mathsf{3}}$$
$$\Qm{3}{0}{2}$$
$$\dofq{4}{2}{0}{0}{1} \pl \dofq{4}{2}{1}{1}{2} \pl \dofq{1}{2}{2}{2}{4} = 16$$
("Q", quadrilateral, 3)
("Q-", quadrilateral, 3, 0)
$$\mathsf{RTc}^{\mathsf{[e/f]}}_{\mathsf{1}}$$
$$\Qm{1}{1}{2}$$
$$\dofq{4}{0}{0}{1}{1} = 4$$
("RTC[E,F]", quadrilateral, 1)
("Q-", quadrilateral, 1, 1)
$$\mathsf{Nc}^{\mathsf{f}}_{\mathsf{1}}$$
$$\Qm{1}{2}{3}$$
$$\dofq{6}{0}{0}{2}{1} = 6$$
("NCF", hexahedron, 1)
("Q-", hexahedron, 1, 2)
$$\mathsf{Nc}^{\mathsf{e}}_{\mathsf{3}}$$
$$\Qm{3}{1}{3}$$
$$\dofq{12}{2}{0}{1}{3} \pl \dofq{6}{2}{1}{2}{12} \pl \dofq{1}{2}{2}{3}{36} = 144$$
("NCE", hexahedron, 3)
("Q-", hexahedron, 3, 1)
$$\mathsf{dQ}_{\mathsf{0}}$$
$$\Qm{1}{1}{1}$$
$$\dofq{1}{0}{0}{1}{1} = 1$$
("DQ", interval, 0)
("Q-", interval, 1, 1)
$$\mathsf{RTc}^{\mathsf{[e/f]}}_{\mathsf{2}}$$
$$\Qm{2}{1}{2}$$
$$\dofq{4}{1}{0}{1}{2} \pl \dofq{1}{1}{1}{2}{4} = 12$$
("RTC[E,F]", quadrilateral, 2)
("Q-", quadrilateral, 2, 1)
$$\mathsf{Q}_{\mathsf{2}}$$
$$\Qm{2}{0}{3}$$
$$\dofq{8}{1}{0}{0}{1} \pl \dofq{12}{1}{1}{1}{1} \pl \dofq{6}{1}{2}{2}{1} \pl \dofq{1}{1}{3}{3}{1} = 27$$
("Q", hexahedron, 2)
("Q-", hexahedron, 2, 0)
$$\mathsf{RTc}^{\mathsf{[e/f]}}_{\mathsf{3}}$$
$$\Qm{3}{1}{2}$$
$$\dofq{4}{2}{0}{1}{3} \pl \dofq{1}{2}{1}{2}{12} = 24$$
("RTC[E,F]", quadrilateral, 3)
("Q-", quadrilateral, 3, 1)
$$\mathsf{Q}_{\mathsf{1}}$$
$$\Qm{1}{0}{1}$$
$$\dofq{2}{0}{0}{0}{1} = 2$$
("Q", interval, 1)
("Q-", interval, 1, 0)
$$\Qm{1}{0}{2}$$
$$\dofq{4}{0}{0}{0}{1} = 4$$
("Q", quadrilateral, 1)
("Q-", quadrilateral, 1, 0)
$$\mathsf{dQ}_{\mathsf{2}}$$
$$\Qm{3}{3}{3}$$
$$\dofq{1}{2}{0}{3}{27} = 27$$
("DQ", hexahedron, 2)
("Q-", hexahedron, 3, 3)
$$\Qm{3}{2}{2}$$
$$\dofq{1}{2}{0}{2}{9} = 9$$
("DQ", quadrilateral, 2)
("Q-", quadrilateral, 3, 2)
$$\Qm{1}{3}{3}$$
$$\dofq{1}{0}{0}{3}{1} = 1$$
("DQ", hexahedron, 0)
("Q-", hexahedron, 1, 3)
$$\mathsf{dQ}_{\mathsf{1}}$$
$$\Qm{2}{1}{1}$$
$$\dofq{1}{1}{0}{1}{2} = 2$$
("DQ", interval, 1)
("Q-", interval, 2, 1)
$$\Qm{2}{3}{3}$$
$$\dofq{1}{1}{0}{3}{8} = 8$$
("DQ", hexahedron, 1)
("Q-", hexahedron, 2, 3)
$$\Qm{2}{2}{2}$$
$$\dofq{1}{1}{0}{2}{4} = 4$$
("DQ", quadrilateral, 1)
("Q-", quadrilateral, 2, 2)
$$\Qm{1}{2}{2}$$
$$\dofq{1}{0}{0}{2}{1} = 1$$
("DQ", quadrilateral, 0)
("Q-", quadrilateral, 1, 2)
$$\Qm{2}{0}{1}$$
$$\dofq{2}{1}{0}{0}{1} \pl \dofq{1}{1}{1}{1}{1} = 3$$
("Q", interval, 2)
("Q-", interval, 2, 0)
$$\mathsf{Nc}^{\mathsf{e}}_{\mathsf{1}}$$
$$\Qm{1}{1}{3}$$
$$\dofq{12}{0}{0}{1}{1} = 12$$
("NCE", hexahedron, 1)
("Q-", hexahedron, 1, 1)
$$\Qm{3}{0}{3}$$
$$\dofq{8}{2}{0}{0}{1} \pl \dofq{12}{2}{1}{1}{2} \pl \dofq{6}{2}{2}{2}{4} \pl \dofq{1}{2}{3}{3}{8} = 64$$
("Q", hexahedron, 3)
("Q-", hexahedron, 3, 0)
$$\Qm{3}{1}{1}$$
$$\dofq{1}{2}{0}{1}{3} = 3$$
("DQ", interval, 2)
("Q-", interval, 3, 1)
$$\mathsf{Nc}^{\mathsf{e}}_{\mathsf{2}}$$
$$\Qm{2}{1}{3}$$
$$\dofq{12}{1}{0}{1}{2} \pl \dofq{6}{1}{1}{2}{4} \pl \dofq{1}{1}{2}{3}{6} = 54$$
("NCE", hexahedron, 2)
("Q-", hexahedron, 2, 1)
$$\Qm{2}{0}{2}$$
$$\dofq{4}{1}{0}{0}{1} \pl \dofq{4}{1}{1}{1}{1} \pl \dofq{1}{1}{2}{2}{1} = 9$$
("Q", quadrilateral, 2)
("Q-", quadrilateral, 2, 0)
$$\mathsf{Nc}^{\mathsf{f}}_{\mathsf{3}}$$
$$\Qm{3}{2}{3}$$
$$\dofq{6}{2}{0}{2}{9} \pl \dofq{1}{2}{1}{3}{54} = 108$$
("NCF", hexahedron, 3)
("Q-", hexahedron, 3, 2)
$$\Qm{3}{0}{1}$$
$$\dofq{2}{2}{0}{0}{1} \pl \dofq{1}{2}{1}{1}{2} = 4$$
("Q", interval, 3)
("Q-", interval, 3, 0)
$$\Qm{1}{0}{3}$$
$$\dofq{8}{0}{0}{0}{1} = 8$$
("Q", hexahedron, 1)
("Q-", hexahedron, 1, 0)
$$\mathsf{Nc}^{\mathsf{f}}_{\mathsf{2}}$$
$$\Qm{2}{2}{3}$$
$$\dofq{6}{1}{0}{2}{4} \pl \dofq{1}{1}{1}{3}{12} = 36$$
("NCF", hexahedron, 2)
("Q-", hexahedron, 2, 2)
$$\mathsf{dPc}_{\mathsf{3}}$$
$$\S{3}{3}{3}$$
$$\dofs{1}{3}{0}{3}{20} = 20$$
("DPC", hexahedron, 3)
("S", hexahedron, 3, 3)
$$\mathsf{S}_{\mathsf{1}}$$
$$\S{1}{0}{1}$$
$$\dofs{2}{1}{0}{0}{1} = 2$$
("S", interval, 1)
("S", interval, 1, 0)
$$\S{1}{0}{2}$$
$$\dofs{4}{1}{0}{0}{1} = 4$$
("S", quadrilateral, 1)
("S", quadrilateral, 1, 0)
$$\mathsf{S}_{\mathsf{2}}$$
$$\S{2}{0}{2}$$
$$\dofs{4}{2}{0}{0}{1} \pl \dofs{4}{0}{1}{1}{1} = 8$$
("S", quadrilateral, 2)
("S", quadrilateral, 2, 0)
$$\mathsf{S}_{\mathsf{3}}$$
$$\S{3}{0}{2}$$
$$\dofs{4}{3}{0}{0}{1} \pl \dofs{4}{1}{1}{1}{2} = 12$$
("S", quadrilateral, 3)
("S", quadrilateral, 3, 0)
$$\mathsf{dPc}_{\mathsf{2}}$$
$$\S{2}{1}{1}$$
$$\dofs{1}{2}{0}{1}{3} = 3$$
("DPC", interval, 2)
("S", interval, 2, 1)
$$\mathsf{BDMc}^{\mathsf{[e/f]}}_{\mathsf{2}}$$
$$\S{2}{1}{2}$$
$$\dofs{4}{2}{0}{1}{3} \pl \dofs{1}{0}{1}{2}{2} = 14$$
("BDMC[E,F]", quadrilateral, 2)
("S", quadrilateral, 2, 1)
$$\S{2}{2}{2}$$
$$\dofs{1}{2}{0}{2}{6} = 6$$
("DPC", quadrilateral, 2)
("S", quadrilateral, 2, 2)
$$\mathsf{dPc}_{\mathsf{1}}$$
$$\S{1}{1}{1}$$
$$\dofs{1}{1}{0}{1}{2} = 2$$
("DPC", interval, 1)
("S", interval, 1, 1)
$$\S{2}{3}{3}$$
$$\dofs{1}{2}{0}{3}{10} = 10$$
("DPC", hexahedron, 2)
("S", hexahedron, 2, 3)
$$\S{3}{1}{1}$$
$$\dofs{1}{3}{0}{1}{4} = 4$$
("DPC", interval, 3)
("S", interval, 3, 1)
$$\S{3}{0}{3}$$
$$\dofs{8}{3}{0}{0}{1} \pl \dofs{12}{1}{1}{1}{2} = 32$$
("S", hexahedron, 3)
("S", hexahedron, 3, 0)
$$\mathsf{AA}^{\mathsf{f}}_{\mathsf{3}}$$
$$\S{3}{2}{3}$$
$$\dofs{6}{3}{0}{2}{10} \pl \dofs{1}{1}{1}{3}{12} = 72$$
("AAF", hexahedron, 3)
("S", hexahedron, 3, 2)
$$\mathsf{AA}^{\mathsf{f}}_{\mathsf{2}}$$
$$\S{2}{2}{3}$$
$$\dofs{6}{2}{0}{2}{6} \pl \dofs{1}{0}{1}{3}{3} = 39$$
("AAF", hexahedron, 2)
("S", hexahedron, 2, 2)
$$\mathsf{BDMc}^{\mathsf{[e/f]}}_{\mathsf{3}}$$
$$\S{3}{1}{2}$$
$$\dofs{4}{3}{0}{1}{4} \pl \dofs{1}{1}{1}{2}{6} = 22$$
("BDMC[E,F]", quadrilateral, 3)
("S", quadrilateral, 3, 1)
$$\mathsf{AA}^{\mathsf{e}}_{\mathsf{3}}$$
$$\S{3}{1}{3}$$
$$\dofs{12}{3}{0}{1}{4} \pl \dofs{6}{1}{1}{2}{6} = 84$$
("AAE", hexahedron, 3)
("S", hexahedron, 3, 1)
$$\S{2}{0}{3}$$
$$\dofs{8}{2}{0}{0}{1} \pl \dofs{12}{0}{1}{1}{1} = 20$$
("S", hexahedron, 2)
("S", hexahedron, 2, 0)
$$\S{1}{3}{3}$$
$$\dofs{1}{1}{0}{3}{4} = 4$$
("DPC", hexahedron, 1)
("S", hexahedron, 1, 3)
$$\S{1}{2}{2}$$
$$\dofs{1}{1}{0}{2}{3} = 3$$
("DPC", quadrilateral, 1)
("S", quadrilateral, 1, 2)
$$\S{1}{0}{3}$$
$$\dofs{8}{1}{0}{0}{1} = 8$$
("S", hexahedron, 1)
("S", hexahedron, 1, 0)
$$\S{3}{2}{2}$$
$$\dofs{1}{3}{0}{2}{10} = 10$$
("DPC", quadrilateral, 3)
("S", quadrilateral, 3, 2)
$$\mathsf{BDMc}^{\mathsf{[e/f]}}_{\mathsf{1}}$$
$$\S{1}{1}{2}$$
$$\dofs{4}{1}{0}{1}{2} = 8$$
("BDMC[E,F]", quadrilateral, 1)
("S", quadrilateral, 1, 1)
$$\mathsf{AA}^{\mathsf{e}}_{\mathsf{2}}$$
$$\S{2}{1}{3}$$
$$\dofs{12}{2}{0}{1}{3} \pl \dofs{6}{0}{1}{2}{2} = 48$$
("AAE", hexahedron, 2)
("S", hexahedron, 2, 1)
$$\mathsf{AA}^{\mathsf{e}}_{\mathsf{1}}$$
$$\S{1}{1}{3}$$
$$\dofs{12}{1}{0}{1}{2} = 24$$
("AAE", hexahedron, 1)
("S", hexahedron, 1, 1)
$$\mathsf{AA}^{\mathsf{f}}_{\mathsf{1}}$$
$$\S{1}{2}{3}$$
$$\dofs{6}{1}{0}{2}{3} = 18$$
("AAF", hexahedron, 1)
("S", hexahedron, 1, 2)
$$\S{2}{0}{1}$$
$$\dofs{2}{2}{0}{0}{1} \pl \dofs{1}{0}{1}{1}{1} = 3$$
("S", interval, 2)
("S", interval, 2, 0)
$$\S{3}{0}{1}$$
$$\dofs{2}{3}{0}{0}{1} \pl \dofs{1}{1}{1}{1}{2} = 4$$
("S", interval, 3)
("S", interval, 3, 0)