From a traditional terminology to an adapted one

Longitudinally plicate (outer wall)

Plicate wall: Each intersept is individually folded formed sharp mid-interseptal longitudinal ridge.

Outer wall: External part of the skeleton, composed by a porous carcass, simple or coated by an additional sheath.

Intersept: Part of a wall or intervallum between two adjacent radial vertical structures (septa, taeniae)

Longitudinally plicate (inner wall)

Plicate wall: Each intersept is individually folded formed sharp mid-interseptal longitudinal ridge.

Inner wall: Internal part of the skeleton, separating central cavity and skeletal structures, composed by a porous carcass, simple or coated by an additional sheath.

Intersept: Part of a wall or intervallum between two adjacent radial vertical structures (septa, taeniae)

Central cavity: Inner space delimited by the inner wall of two-walled cup. In one-walled cup = inner cavity.

Outer wall shows folds

Fold: Succession of more or less regular annulations of cup.

Outer wall: External part of the skeleton, composed by a porous carcass, simple or coated by a additional sheath.

Inner Wall shows folds

Fold: Succession of more or less regular annulations of cup.

Inner wall: Internal part of the skeleton, separating central cavity and skeletal structures, composed by a porous carcass, simple or coated by an additional sheath.

Central cavity: Inner space delimited by the inner wall of two-walled cup. In one-walled cup = inner cavity.

Both walls show folds

Fold: Succession of more or less regular annulations of both walls.

None

isn't included in the term

Hierarchy

structure
 |
 |_ Shape of cup bulges
    |
    |_ Type of folds affecting both walls {Longitudinally plicate (outer wall) , Longitudinally plicate (inner wall) , Outer wall shows folds , Inner Wall shows folds , None , isn't included in the term}