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Darwin Correspondence Project

From E. A. Darwin   [8 June 1858]1

Dear Charles

I find I cannot draw a ⊙ round your diagram two points, as the difference is so small only about a 170 or 80 of an inch.

I send you 2 more projections as the more points of view you see it in the better2

I also send you some rhombs cut out, with flaps to fasten over the edges, & I advise you to begin with the flap (A)3

They are not the same size as Millers,4 & I do not know if you have any reason for that particular size.

Also a pyramid, with 2 circles on the base to be raised up & the circle on the short diameter will show you exactly how much the obtuse ∠’s are within the sphere diagram

12 of these pyramids would make the Dodec.

You will be surprized how firm the model will feel when put together, but dont be in a hurry & let one flap dry before you paste another,

When you have got the model in your hand, & hold them in the same position as my diagrames, they will all become quite clear.

I think I have answered all your questions.


Over the page I will draw another little diagram to fix the positions of the acute ∠s

N E S W equator
S P N P’ meridian
W P E P’ East & West circle
6 acute angles at the letters
8 obtuse angles (A) in the center of the quadrants


[No 1]
AB vertical axis passing thro’ acute ∠s A & B
CD horizontal axis passing thro’ centers of 2 Rhombs
K axis perpendicular to CD & AB or the plane of the paper
a b e f } rhomb parallel to paper, natural size
diameter bf = AC = side of square in ⊙
diameter ae = KA radius of ⊙
a b c d— rhomb oblique to the paper
cb is parallel to ae and = 12 ae or Ke
.:. Kc = eb = side of rhomb

The obtuse ∠ at c is in the plane of the paper

.:. Kc = radius of ⊙ passing thro’ obtuse ∠s

Kb = 12 distance of centers = distance from center of sphere to rhomb
[No 2]
The same as No 1 but turned round the axis AB 45o.
The 4 rhombs are all at ∠ 45o with paper, but fAfB are the long diameter of the vertical plane, & fC, fD long diameters in the horizontal plane


Dated by the postmark on a cover associated with the letter (DAR 162: 50).
See enclosure.
The figures have not been found.
See letter from W. H. Miller, [14 May 1858] and n. 2. Associated with William Hallowes Miller’s letter are two pasteboard figures labelled ‘Rhombic face of dodecahedron’ (DAR 48 (ser. 2): 1). The angles of the rhombs are marked ‘70o 31.7’’ and ‘109o 28.3’’. See Natural selection, p. 513 and n. 1, where the angles of a rhombic face of a bee’s cell are discussed.
The diagrams are in DAR 162: 48/5 and 48/6.


Natural selection: Charles Darwin’s Natural selection: being the second part of his big species book written from 1856 to 1858. Edited by R. C. Stauffer. Cambridge: Cambridge University Press. 1975.


Encloses projections and models relating to geometry of bees’ cells.

Letter details

Letter no.
Erasmus Alvey Darwin
Charles Robert Darwin
Sent from
Source of text
DAR 162: 48a, 50
Physical description
ALS 4pp, encl 3pp

Please cite as

Darwin Correspondence Project, “Letter no. 2283,” accessed on 1 June 2023,

Also published in The Correspondence of Charles Darwin, vol. 7