Square antiprism (EntityTopic, 13)

From Hi.gher. Space

The square antiprism is a special case of an antiprism where the base is a square.


  • The planar cross-sections of a square antiprism in the [!z] plane are octagons, giving a regular octagon in the middle and degenerating to squares at the ends.
  • The planar cross-sections of a square antiprism in the [!x] and [!y] planes are irregular pentagons, degenerating to trapeziums in the middle and at the ends.

Incidence matrix

Dual: tetragonal trapezohedron

0 Va = point ;
1 Ea 2 = digon ;
2 Eb 2 = digon ;
3 4a 440 = square ;
4 3a 312 = triangle ;
5 C1a 88828 = square antiprism ;

Usage as facets

Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind