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Darwin Correspondence Project

From W. H. Miller   [14 May 1858]1

[Enclosure 1]2}

For constructing model of bees cell of bristol board— With aid of card rhomb3 construct a figure like this—but with much more accuracy— on thin bristol board cut completely through in the black lines—and half through with sharp pointed knife applied to edge of a ruler—in the blue lines— I believe no further explanation is requisite—

or try it in thick paper folding in the blue lines and cutting in the black lines.4

[Enclosure 2]

Dodecahedron net traced from a plate in the Einleitung in die Krystallographie of Hermann Kopp.5


Figure of a dodecahedron. It may be converted into the figure of a cell by prolonging either the 6 lines parallel to A, or the 6 lines parallel to B.



The date is that of the postmark on the accompanying cover. It is not clear, however, whether the cover belongs with the material now enclosed in it (see nn. 2 and 3, below).
The two enclosures transcribed here are in a cover with other items, all of which relate to the geometry of bees’ cells. One is a model for a bee’s cell based upon a rhombic dodecahedron, which may have been made by William Erasmus Darwin (see letter to W. E. Darwin, [23 May 1858]). No covering letter from Miller has been located.
The ‘card rhomb’ to which Miller refers is with these instructions in DAR 48 (ser. 2): 1. There is also another similar cardboard figure marked by Miller: ‘This is not very accurately drawn.’ Both figures represent the rhombic face of a dodecahedron and were labelled as such by Miller. The angles are also given.
These instructions were written on a large piece of tissue paper on which Miller had sketched a rough plan for constructing a model of a bee’s cell based on part of an elongated rhombic dodecahedron. Miller indicated the sections to be folded and glued together. Miller’s first attempts to represent a bee’s cell had been erroneous (see letter to W. E. Darwin, [3 May 1858]). CD had enlisted Miller’s assistance after realising that there were problems with the geometry of George Robert Waterhouse’s theory (see letter from G. R. Waterhouse, 13 February 1858 and letter to W. H. Miller, [15 April 1858]). In his notes on [Waterhouse] 1835 (DAR 48 (ser. 2): 66a), CD remarked: ‘W. did not get aid of mathematician, [as curious] & necessary advantage which I owe to kindness of Professor Miller of Cambridge.’ See Origin, p. 226, where CD expressed his indebtedness to Miller for calculations relating to bees’ cells.
Kopp 1849.


[Six fragments, mainly diagrams.] The geometry of bees’ cells.

Letter details

Letter no.
William Hallowes Miller
Charles Robert Darwin
Sent from
Source of text
DAR 48: B1b
Physical description
diags 6pp

Please cite as

Darwin Correspondence Project, “Letter no. 2272,” accessed on 19 April 2019,

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