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The key to the dissected flower images is here.

1a Stems 1.75 - 3+ m. Leaves spread regularly up the stem. 10 - 30+ flowers. Flower bracts lost before flower is fully open. Flowers show no zygomorphism. 2

1b Stems 0.5 - 1.75m. Leaves not spread regularly up the stem. 3 - 20 flowers. Flowers retain the lower flower bract for some time after opening. Flowers show slight to pronounced zygomorphism about a horizontal plane, (the Cordatum hump). 5

2a Stems green, robust. Flowers have a green tinge, which becomes cream in full sun, with slight to medium bands of magenta on the adaxial surfaces of the sepals and petals and faint colour on the abaxial surface of the petals. Never white. The corolla is not divided. Cardiocrinum giganteum v. giganteum .

2b Stems darker green, sometimes streaked with or completely purple, more gracile. Flowers have no more than a slight green tinge. Corolla is divided on mature flowers. 3

3a Flowers are white with varying amounts of magenta. 4

3b Flowers are completely magenta with no white. Cardiocrinum giganteum v. yunnanense 'Big and Pink' [1] The Far Reaches Nursery cultivar, ( or a new sport?).

4a Flowers are white with slight to strong bands of magenta mainly on the adaxial surfaces of the sepals and petals but some on the abaxial surface of the petals. The corolla tends to be divided on the mature flower. Cardiocrinum giganteum v. yunnanense . [2]

4b Flowers are completely white with no trace of magenta. Cardiocrinum giganteum v. yunnanense f. alba . [3]

5a Few flowers, (3 - 7), collected in China.[4] Cardiocrinum cathayanum

5b Collected in Japan.[5] 6

6a Stem usually 0.5 - 1.25m. Few flowers, (3 - 7). Cardiocrinum cordatum .

6b Tall, more robust stem to 1.75m. Up to 20 flowers. Cardiocrinum cordatum v. glehnii .

[1, 3] It isn't certain that these taxa are stable.
[2] This will include Cardiocrinum cathayanum (hort.)
[4] These are most unsatisfactory criteria and I'd welcome any information which would provide better!