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Cahill Butterfly Map 1909

Cahill-Keyes M-layout world map silhouette including
Cahill 1909
Cahill-Keyes 1975

Note: being averse to small print, I composed this in an 8" frame with ca. 12 pt. serif type. If you are like me, you may wish to enlarge your screen view to show a similar frame and font size, in case there is a puny default.

B.J.S. Cahill Butterfly Map
Online Resource:
Octahedral Map of the World

Compiled by Gene Keyes

21st Edition 2015-04-14, revised and updated; more to come
The Octahedral Butterfly Map of the World, by Bernard J. S. Cahill (1866-1944), first published in 1909, is a sadly neglected masterpiece of world map design. This resource presents some of Cahill's articles, manuscripts, and Butterfly map variants, which he continued to develop during three more decades until 1940. Also included here are post-Cahill maps by Buckminster Fuller; Steve Waterman; and my own re-working of Cahill's octahedral creation.
Cahill's original 1909 Butterfly World Map

These hotlinks scroll down to a subsection,
whose links open each listing on a separate page

1) B.J.S. Cahill himself

1.0) Photos

1.1) Publications

1.2) Unpublished (but online) material

1.3) Cahill octahedral world map images

1.4) Articles about Cahill octahedral map

1.5) Cahill archive listings

1.6) Other references (tba): not, or not yet, online

2) Post-Cahill

2.1) Buckminster Fuller (Dymaxion Map, 1943, 1954; non-Cahill)

2.2) Gene Keyes (Cahill-Keyes Multi-scale Megamap, 1975 ff)

2.3) Steve Waterman (Waterman Butterfly Map, 1996 ff)

1) B.J.S. Cahill himself

1.0) Photos

To triple this image size, click once. To restore smaller size, click twice. Note: in triple size, you can see the mapwork on the polygon; and at the far right, a corner of his Gnomonic variant.
B.J..S. Cahill
B.J.S. Cahill (1866-1944): Architect and Cartographer

Source: Scanned by Gene Keyes in 2012 from undated duplicate of
photo (ca. 1936?) at Bancroft Library, University of California at Berkeley,
Bernard Joseph Stanislaus Cahill Papers, (83/39)

B.J.S. Cahill, ca. 1940
B.J.S. Cahill, ca. 1940

Source: pdf from Cahill grandchildren; converted to jpeg by GK.

Photos reproduced with permission from the descendants of B.J.S. Cahill:
Laura Cahill Huber, Susan Cahill Aylward, and Stanley James Cahill.

1.1) Online papers and publications by B.J.S. Cahill:
Annotated link-list [still in progress]
  • All items are on this website and open in separate windows;
  • Chronological by earliest composition date;
  • Publication date in boldface.

1909-02 / 1909-09
Cahill, B.J.S., "An Account of a New Land Map of the World" (The Scottish Geographical Magazine, 1909-09) p. 449-469.
The first publication and exposition of the Butterfly Map. Strong critique of Mercator for classrooms.

1912-03-05 / 1913-02-25
Cahill, B.J.S., "Map of the World", U.S. Patent 1,054,2761913 (Washington, DC: United States Patent Office, 1913-02-25; filed 1912-03-05.) 3 p.
Cahill's patent of the Butterfly Map itself. Online here as jpegs, pdf, or HTML.

1912-10 / 1913-10
Cahill, B.J.S., "A Land Map of the World on a New Projection" (Journal of the Association of Engineering Societies, 1913-10; orig. 1912-10) p. 153-207
Cahill's longest and most thoroughgoing published exegisis of his Butterfly Map; also includes 50 illustrations, 20 of which are a comparison of various map projections to the same scale using the same size globe-circle for each. Over three decades before Buckminster Fuller’s 1943 Dymaxion map, Cahill had already created a far more elegant octahedral world map, and shown how it is designed for thinking “planetarily”. Article is re-formatted in HTML with all the illustrations.

1913-02-11 / 1913-12-09
Cahill, B.J.S., "Geographic Globe" (Washington, DC: United States Patent Office, 1913-12-09; filed 1913-02-11) 2 p. + extra photo.
Cahill's patent for a rubber-ball globe which can flatten to a Butterfly Map, or return to ball shape. Online here as jpegs, pdf, or HTML.

Cahill, B.J.S., The Butterfly Map: The Surface of the World Shown on an Eight-Part Decentralized Projection (n.d., ca. late 1919 or early 1920) 8 p. illus.
Promotional pamphlet (shown here in 8 jpegs), with
(a) descriptive material and pictures, front and back pages;
(b) reprints of two of his illustrated articles, deprecating the Mercator map;
(c) three pages of blurbs from prominent geographers, educators, and personages of the day (including two by John Paul Goode, who went on to perpetrate the Homolosine three years later).

1928-12-28 / 1929-04
Cahill, B.J.S., "Projections for World Maps"
—and text continued in separate pdf, plus illustrations:—
Cahill, B.J.S., "A New Map for Meteorologists: Equally Suitable for Small Areas, Continents, Hemispheres or the Entire World" – both from Monthly Weather Review, 57/4, 1929-04) p. 128-133; illus.
Has Cahill's only published [partial] world map with a one-degree graticule, except on land areas; as well, one of his only published five-degree world maps, regrettably discontinuous on two pages. See similar map in [1934] below, octants together, but in an awkward north-south spread, which I also show enlarged; and cf [1940] below, in Butterfly layout.
Pdf's are re-posted on my page via above links for convenience; source URLs were:

Cahill, B.J.S., "A World Map to End World Maps" (Geografiska Annaler, 1934) p. 97-108.
Argues against proliferation of arcane projections, and sets forth three major Variants to improve upon his original design: Conformal, Equal Area, and Gnomonic, within his basic octahedral framework. "When finally map and globe practically agree . . . the need of further world mapping comes naturally to an end."

1940-04-03; 1940-05-20
Cahill, B.J.S., "One Base Map in Place of Five" (1940) Monthly Weather Review, 68/2, 1940-02 [1940-05-20], p.4; 1 illus.
Again urges the meteorological community to display data on a single world map, his Conformal Variant. Unlike items 6 and 7 above, here the map is shown in its customary Butterfly profile, Pacific aspect. This was Cahill's final article; he died in 1944 after a long illness.
Pdf re-posted on my page via above link for convenience; source URL was

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1.2) Unpublished Material by B.J.S. Cahill:

1939; 2011-10-01
Cahill, B.J.S., "The Butterfly Map of the World Today" (Typescript, [1939] edited and formatted in HTML and with Foreword by Gene Keyes) 54 p.
Unpublished and unfinished book typescript: history, vicissitudes, and prospects for Cahill's octahedral map system. Lightly edited by gk for typos, etc.

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1.3) Cahill octahedral world map images
(scanned and compiled by GK)

A Comparative Gallery of 25 Cahill (and later) octahedral maps [1st ed.]

Cahill's largest world map: an analysis with full size online images

B.J.S. Cahill's Butterfly World Map: Five Desk Versions
(Updated with fifth map, 2015-03-31.)

• Cahill's "Variants" clarified [tba]

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1.4) Articles about Cahill octahedral map
[Both are in same link, but reverse order.]

[Kaempffert, Waldemar?], "Mapping the Sphere on a Plane" (Scientific American, 1913-07-26)
Lauds Cahill map as "the best attempt so far to map the globe on a plane."

Kaempffert, Waldemar, "True World Maps: Cahill Projections Drawn Like Patterns for the Globe" (New York Times, 1943-03-14)
An ineffectual description, as if to counter Life Magazine's debut of Buckminster Fuller's Dymaxion map two weeks earlier (1943-03-01). Too little, too late.

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1.5) Cahill archive listings

Three archives at University of California, Berkeley

Digitized listing of Cahill map collection at Bancroft Library, U.Cal. Berkeley

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2) Post-Cahill

2.1) Buckminster Fuller (Dymaxion Map, 1943, 1954: non-Cahill)

Why Cahill? What about Buckminster Fuller?

Fuller icosahedral map 1954

Keyes, Gene, Evolution of the Dymaxion Map: An Illustrated Tour and Critique [on 17 interlinked Web pages].

Summary: I love Bucky, but Cahill's map is a lot better. Here's how.

Detailed discussion with profusely illustrated comparison of Fuller and Cahill maps. Includes first online image of Cahill's unpublished but significant 1936
Equal Area Variant "C" (fig. 9.2.1).

2.2) Gene Keyes (Cahill-Keyes Multi-scale Megamap, 1975 ff)

Mapwork of Gene Keyes, inspired by Cahill (and Fuller)

Go to complete linklist of Cahill-Keyes map development

For more details and much bigger images of this map, click in it.

Cahill-Keyes Multi-scale Megamap Beta-2, preview

Map drafts

Hand-produced 5-degree 1975 version (jpegs of 1980 offset-print):

Here and

Here (both smaller, 1/200 M), and

Here (larger, 1/100 M)

Hand-produced one-degree king-size prototypes, 1975-1983:

Computer-drawn one-degree versions, 2011 ff

Beta-1 Digital Version: Cahill-Keyes Multi-scale Megamap )


Cahill-Keyes 5° Globe & Megamap Beta-2 Preview


10 screenshots of Cahill-Keyes Megamap Beta-2, & 4 full-size pdf's: 1/1 M, + 10, 50, & 100 M Update 2014-01-23: The gym-size 1/1 M Megamap, a 35 MB pdf, can now be easily and quickly panned, without the user getting lost, by opening it in the freeware Foxit pdf reader.


Presenting the Cahill-Keyes 1° Globe: World's first and only Earth-globe drawn with a 1° graticule

Around the world in 8 easy pieces: Cahill-Keyes 1° globe (full size images of all 8 octants)

• Offset-print poster version of Duncan Webb's 61" Cahill-Keyes Wall Map published and now available: order here ($65 US)

Zooming to Crimea in the Cahill-Keyes Multi-Scale Megamap, Beta-2: How to easily view a 9,000 square foot Megamap pdf without getting lost: panning & re-sizing with free Foxit reader

Cahill-Keyes World Map by Others: A gallery of 9 different versions: published, and drafts in progresss

Design notes
1982 . . . 2011
"Notes on Scaling Cahill and Cahill-Keyes Maps"

"Notes on Re-designing B.J.S. Cahill's Butterfly World Map"

1980 . . . 2010-02-05
"Cahill-Keyes Octant Graticule X-Y Coordinates and Segment Lengths (scaffold triangle and perimeter only)

2010 . . . 2012-02-09
"Cahill-Keyes Octant Graticule: Principles and Specifications (with Perl programs and OpenOffice.org 2.0 Draw macros for 1/1,000,000 Megamap)"

"Toward a Computerized World Coastline for the Cahill-Keyes Octant Graticule" (2011)

Beta-1 Digital Version: Cahill-Keyes Multi-scale Megamap

• Mary Jo Graça's updated Perl script for Beta-2: enables octant rotation, and contiguous extensions for Antarctica, Russian Far East, Iceland, etc.  (Downloadable at that page, or directly online as uploaded by Enrico Spinielli.)

Progress Reports
 • Large test prints and corresponding globe with 5° geocells

Cahill-Keyes 5° Globe & Megamap Beta-2 Preview


1973-09-10 . . . 2009-07-18
"10 Principles for a Coherent World Map System"

1983-05-07 . . . 2013-09-19
"Geocells and the Megamap"


since 2007-04-17 ff
• B.J.S. Cahill Online Resource
(you are already looking at it)

New York Times' adaptation of Cahill-Keyes for 10 thematic maps

 Nick Stockton, "Gene Keyes's 40-Year Quest for the Perfect Map", Wired.com (Erratum: projection is not "octal gradient", but "Cahill-Keyes Octant Graticule")

and similar article:

Wesley Fenlon, "The Cahill-Keyes Megamap: Accuracy 40 Years in the Making", [Mythbusters]

2.3) Steve Waterman (Waterman Butterfly Map, 1996)

Cahill-similar mapwork of Steve Waterman

[GK] Review of Waterman World Map
My review is favorable toward this Cahill-like Butterfly map, but demurs at its separate Antarctica cut-out, and some erroneous Arctic coastlines. It also details points of difference between his design and graticule, and mine. [A newer and improved version of the Waterman has since been issued, in 2012.]

Waterman map, postcard version

Go back to Gene Keyes home page