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It seems face connectivity for triangle element depends upon the interpolation.
Make it cyclic. That is use cyclic edge master element for hierarchical and orthogonal polynomials on triangle.
MODULE PROCEDURE FacetConnectivity_Triangle
CHARACTER(3) :: bi
bi = UpperCase(baseInterpol(1:3))
SELECT CASE (bi)
CASE ("HIE", "HEI", "ORT")
ans(:, 1) = [1, 2]
ans(:, 2) = [1, 3]
ans(:, 3) = [2, 3]
CASE DEFAULT
ans(:, 1) = [1, 2]
ans(:, 2) = [2, 3]
ans(:, 3) = [3, 1]
END SELECT
END PROCEDURE FacetConnectivity_Triangle