There are many types of daffodils in the world, and to keep things organized, they are all classified according one particular system;
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The RHS Horticultural Classification.
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Below you will and an overview of what the various divisions mean, how you can determine to which division your daffodil belongs to, and how the colour coding system works.
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Division 1 - Trumpet Daffodils
One flower to a stem; corona (“trumpet”) as long as, or longer than the perianth segments (“petals”)
Division 2 - Large-Cupped Daffodils
One flower to a stem; corona (“cup”) more than one-third, but less than equal to the length of the perianth segments (“petals”)
Division 3 - Small-Cupped Daffodils
One flower to a stem; corona (“cup”) not more than one-third the length of the perianth segments (“petals”)
Division 4 - Double Daffodils
One or more flowers to a stem, with doubling of the perianth segments or the corona or both
Division 5 - Triandrus Daffodils
Characteristics of N. triandrus clearly evident: usually two or more pendent flowers to a stem; perianth segments reflexed
Division 6 - Cyclamineus Daffodils
Characteristics of N. cyclamineus clearly evident: one flower to a stem; perianth segments significantly reflexed; flower at an acute angle to the stem, with a very short pedicel (“neck”)
Division 7 - Jonquilla Daffodils
Characteristics of Sections Jonquilla clearly evident: one to five (rarely eight) flowers to a stem; perianth segments spreading or reflexed; corona cup-shaped, funnel-shaped or flared, usually wider than long; flowers usually fragrant
Division 8 - Tazetta Daffodils
Characteristics of Section Tazettae clearly evident: usually three to twenty flowers to a stout stem; perianth segments spreading not reflexed; flowers usually fragrant
Division 9 - Poeticus Daffodils
Characteristics of N. poeticus and related species clearly evident; perianth segments pure white; corona very short or disc-shaped, not more than one-fifth the length of the perianth segments; corona usually with a green and/or yellow centre and red rim, but sometimes wholly or partly of other colours; anthers usually set at two distinct levels; flowers fragrant
Division 10 - Bulbocodium Daffodils
Characteristics of Section Bulbocodium clearly evident: usually one flower to a stem; perianth segments insignificant compared with the dominant corona; anthers dorsifixed (ie attached more or less centrally to the filament); filament and style usually curved
Division 11a and 11b - Split-Corona Daffodils
a) Collar Daffodils Split-corona daffodils with the corona segments opposite the perianth segments; the corona segments usually in two whorls of three
b) Papillon Daffodils Split-corona daffodils with the corona segments alternate to the perianth segments; the corona segments usually in a single whorl of six
Division 12 - Other Daffodils
Daffodil cultivars which do not fit the definition of any other division
Division 13 - DAFFODILS DISTINGUISHED SOLELY BY BOTANICAL NAME
One flower to a stem; corona (“trumpet”) as long as, or longer than the perianth segments (“petals”)