"SnoVolution"

Our sculpture, a volution-shell in snow,
emerges from an evolution of simpler volution shells.
It represents a conceptual revolution in the sense of
last year's "Rêve'Olution" performed by the team from Quebec.
A convolution of tunnels and saddles can form a surface of genus 5.
The involution of the resulting "jungle-gym" geometry is then reduced
by a devolution of a corrsponding triangle mesh to a minimal surface,
using Brakke's Surface Evolver.

The simples Volution shell of genus 0, homomorphic to a simple disk.

If we add a single handle to the disk and symmetrize the region underneath ...

we obtain a Volution shell of genus 1, exhibiting two touching tunnels.

Adding four more tunnels results in the genus-5 Volution shell.

This seems to be about the right complexity for a snow sculpture.
It seems to be of about the same fragility as the "Whirled White Web"
and only slightly more complex. Seen as a 3D object, it is of genus 10;
compared to the "WWW" which was of genus 7.
To understand this different viewpoint, consider the disk_with_one_handle above:

When thickened to a 3D object, it then has a rimless surface of genus 2.

The genus-5 volution shell can be positioned in two different ways on the pedestal:

Version A places one of its C2-symmetry axes in the up direction, giving front-to-back symmetry.

Version B places the same shape on one of its sides and then gives four different views.

Page Editor: Carlo H. Séquin