Celestials of Moebius degree 4

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The images were made using Sage and Surfex.

See [2] for the definition of Euclidean type. The isolated singularities of celestials are denoted by their Dynkin type .

Blum cyclide, no isolated singularities, 6 families

Euclidean type (3,1)

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Euclidean type (4,2)

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sphere cyclide, no isolated singularities, 2 families

Euclidean type (3,1)

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Euclidean type (4,2)

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cyclide with two components, no isolated singularities, 2 families

Euclidean type (3,1)

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Euclidean type (4,2)

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Perseus cyclide, singularities: 2A_1, 5 families

Euclidean type (3,1)

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Euclidean type (4,2)

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Ring torus, singularities: 4A_1, 4 families

Euclidean type (3,1)

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Euclidean type (4,2)

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Multiple circular surface with real singularities

Dynkin type(2,0)(3,1)(4,2)clipping
A_1 (EH1) Picture Picture Picture Picture
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A_1 (E) Picture Picture Picture
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A_1 (EH2) Picture Picture Picture
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2A_1 (EO) Picture Picture Picture
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A_2 (HP) Picture Picture Picture
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A_2 (EP) Picture Picture Picture Picture
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3A_1 (CH1) Picture Picture Picture Picture
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A_3 (EY) Picture Picture Picture Picture
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4A_1 (CO) Picture Picture Picture Picture
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A_3+2A_1 (CY) Picture Picture Picture Picture
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