Polyhedron Category C9: Octahedral Continuums


This category consists of compounds of the octahedron in the form of a triangular antiprism. They form three continuums of flexible compounds that go through various phases. The first continuum has cubic symmetry, it starts with the octahedron which splits into 8 copies and becomes idso, it continues to morph until it reaches the boundary case of hidso where two snub triangles become coplanar. Continuing on it goes into the odso phase and finally the 8 octs merges into four and it becomes sno, it then reverses the process. The second continuum has pyritic symmetry. It also starts with oct which splits into four copies and becomes idsit, it passes the hidsit boundary and becomes odsit on its way back to sno. The next continuum has doic symmetry and goes through the following phases: Start at the 10 oct compound si, which becomes a 20 oct compound oddasi until it reaches the doubled vertex form dasi. Continuing through the iddasi phase and then the 20 octs fuse into 5 at se (category C1). Continuing, it splits back into 20 octs becoming giddasi until it fuses into 10 octs at gissi, it then goes in reverse. All of these are orientable except for sapisseri and their verfs are squares except for the last two.

C54. Sno - (SNO) snub octahedron. Faces are 8 triangles and 24 snub triangles. It is a compound of 4 octs. It has 24 vertices.

C55. Idso - (ID so) inner disnub octahedron. Faces are 16 triangles (paired up) and 48 snub triangles. It is a compound of 8 octs. It has 48 vertices. Idso, hidso, and odso can also be considered as three versions of one compound, that we can call "daso" for disnub octahedron.

C56. Hidso - (HID so) hexagrammic disnub octahedron. Faces are 16 triangles (paired up) and 48 snub triangles (paired up). It is a compound of 8 octs. It has 48 vertices.

C57. Odso - (ODD so) outer disnub octahedron. Faces are 16 triangles (paired up) and 48 snub triangles. It is a compound of 8 octs. It has 48 vertices.

C58. Idsit - (ID sit) inner disnub tetrahedron. Faces are 8 triangles and 24 snub triangles. It is a compound of 4 octs and has 24 vertices. Idsit, hidsit, and odsit can be considered as three versions of one compound that we can call "dissit" for disnub tetrahedron.

C59. Hidsit - (HID sit) hexagrammic disnub tetrahedron. Faces are 8 triangles and 24 snub triangles (paired up). It is a compound of 4 octs and has 24 vertices. This compound can be produced by removing one oct from se (the 5 oct compound).

C60. Odsit - (ODD sit) outer disnub tetrahedron. Faces are 8 triangles and 24 snub triangles. It is a compound of 4 octs and has 24 vertices.

C61. Si - (SI) snub icosahedron. Faces are 20 triangles and 60 snub triangles. It is a compound of 10 octs. It has 60 vertices.

C62. Gissi - (GISS see) great snub icosahedron. Faces are 20 triangles and 60 snub triangles. It is a compound of 10 octs, oriented differently than si. It has 60 vertices.

C63. Oddasi - (ODD a see) outer disnub icosahedron. Faces are 40 triangles (paired) and 120 snub triangles. It is a compound of 20 octs. It has 120 vertices. Oddasi and the next two are sometimes refered to as one compound, however they are in different teepees.

C64. Iddasi - (ID a see) inner disnub icosahedron. Faces are 40 triangles (paired) and 120 snub triangles. It is a compound of 20 octs. It has 120 vertices.

C65. Giddasi - (GID a see) great disnub icosahedron. Faces are 40 triangles (paired) and 120 snub triangles. It is a compound of 20 octs. It has 120 vertices.

C66. Dasi - (DAY zee) disnub icosahedron. Faces are 40 triangles (paired) and 120 snub triangles. It is a compound of 20 octs. It has 60 vertices that are doubled. It and sapisseri are in the same regiment as gidrid. Its verf is a compound of two squares.

C67. Sapisseri - (sa PISS er ee) snub pseudosnub rhombicosahedron. Faces are 12 stars and 60 snub triangles. It is a compound of 20 thahs. It has 60 doubled vertices. Its verf is a compound of two bowties.


All of these are self conjugates.


Category C8: Antiprismatics . . . Polyhedron Page . . . Category C10: Disnubs