THE PATENTS
Left to Right : Click to enlarge : Patents for Shaped Style Sundials -  (i) 1867 US Patent by L.Miflin (ii) 1892 UK Patent by Major John Ryder Oliver.
PIERCED STYLE DIALS
In this class, the each half of the analemma is encoded in either side of the style.
Left to Right : Click to enlarge  (i) Ken Clark - Schmoyer Dial 2018 (ii) 3-D printed Schmoyer dial by Bill Gottesman, www.precisionsundials.com (iii) Tony Moss 'Henry Moore' dial - ca 2010 - note the clever arrangement to ensure that the plane of the analemma is perpendicular to the sun's rays. (iv - v) Pete Swanstrom - www.swanstrom.net/sundial/ - Ann Morrison Park, Boise, Idaho - 1998 and New Millennium Dial - 2018
SHAPED STYLE DIALS
In all cases, in this class, the shape of the analemma (or half of it) is encoded in the style. If the style is symmetrical, it must encode half the analemma. In which case, two interchangeable styles must be provided) - with exceptions (see below)
Left to Right : Click to enlarge  (i - ii) Mean Time Sundials with polar cone and vertical cone gnomons - Hendrix Hollander - www.analemma.nl - ref NASS Compendium v13(3) Sept 2006 - 2 articles : Mean Time Sundial With A Cone Gnomon & Bi-Gnomon Sundials (iii) Rolf Wieland : There are two shaped styles : each representing half the analemma : Ref  NASS Compendium v18(2) June 2011 (iv) Martin Bernhard' s dial at the Stuttgart Planetarium
THE INTEGRATED DOUBLE GNOMON SUNDIAL OF WERNER RIEGLER
This unique idea has been realised in 2003 by Werner Riegler in Joannes Kepler's city of Linz. 
Left to Right : Click to enlarge : (i) The solid inner and transparent outer parts of the Style (ii) the Dial in section, (iii) Detail of the lower half of the dial (iv) How the dial is read in the sun-ascending & sun-descending halves of the year (v) Werner Riegler at the installation.
The dial also contains a calendar. When the time is being read on one side of the dial, one of the two possible dates can be read from the shadow of the dial rim on the other side of the dial. Left to Right : Click to enlarge (i) as modelled (ii) in reality.
Left to Right : Click to enlarge : (i) the top half of the style (ii) the bottom half (iii) the two previous images merged to show the analemma
For more detail, read below
ERRORS USING A SINGLE SYMMETRICAL GNOMON THROUGHOUT THE YEAR
Werner Riegler has analysed this situation in the following paper. In summary, a symmetrical gnomon can be made that will work with errors not exceeding 1.7 minutes of time. However such a gnomon will not work for some 10 days around the winter solstice and for some 2 days around the summer solstice. During these periods, the correction for one day shadows the correction of the next day. Thus, such a gnomon can only exist the declination range -23.30° to 23.42°
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