Lantern

Lantern
(3D model)
Rank	3
Type	Quasi-convex Stewart toroid
Notation
Stewart notation	Q4T4/P4(B4)Q4
Elements
Faces	4+4+4+4+4+4 triangles, 4+4+4+4 squares, 4 octagons
Edges	4+4+4+4+4+4+4+4+4+8+8+8+8+8+8
Vertices	4+4+4+4+4+4+8+8
Measures (edge length 1)
Volume	$6+3{\sqrt {2}}\approx 10.24264$
Surface area	$24+8{\sqrt {2}}+6{\sqrt {3}}\approx 45.70601$
Related polytopes
Convex hull	Augmented truncated cube
Abstract & topological properties
Flag count	336
Euler characteristic	0
Surface	Torus
Orientable	Yes
Genus	1
Properties
Symmetry	B2×I, order 8
Flag orbits	42
Convex	No

The lantern is a quasi-convex Stewart toroid. It can be made by excavating a cube, a cuboctahedron, and a square cupola from a augmented truncated cube. The cuboctahedron and the cube can be switched to obtain a similar but distinct tunnelling.

Gallery

• 

  A view of the tunnel.

External links

• Doskey, Alex. "Chapter 5 - Simplest (R)(A)(Q)(T) Toroids of genus p=1".

Bibliography

• Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.