- Polyhedron as Polyhedra Generator (segments trisection)
- ⓿. Biscribed Pentakis Dodecahedron
- ❶. Rhombicosidodecahedron (V=120) and its dual polyhedron- (V=122) from Biscribed Pentakis Dodecahedron for the case of trisection of its 1st-order segments
- ❷. Truncated dodecahedron (V=60) and its dual polyhedron- Triakis icosahedron (V=32) from Biscribed Pentakis Dodecahedron for the case of trisection of its 2nd-order segments
- ❸. Truncated icosahedron (V=60) and its dual polyhedron- Pentakis dodecahedron (V=32) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments
- ❹. Truncated icosidodecahedron (V=120) and its dual polyhedron- Disdyakis triacontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 4th-order segments
- ❺. Polyhedron(V=120) and its dual polyhedron (V=152) from Biscribed Pentakis Dodecahedron for the case of trisection of its 5th-order segments
- ❻. Polyhedron(V=120) and its dual polyhedron (V=152) from Biscribed Pentakis Dodecahedron for the case of trisection of its 6th-order segments
- ❼. The Great Rhombicosidodecahedron (V=120) and its dual Disdyakis triacontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 7th-order segments
- ❽. Rhombicosidodecahedron (V=60) and its dual Deltoidal Hexecontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 8th-order segments (Variant1)
- ❾. Rhombicosidodecahedron (V=60) and its dual Deltoidal Hexecontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th-order segments(Variant2)
- ❿. Polyhedron(V=120) and its dual Polyhedron(V=152) from Biscribed Pentakis Dodecahedron for the case of trisection of its 10th-order segments
- ⓫. Biscribed Pentakis Dodecahedron (V=32) and its dual Biscribed Truncated Icosahedron(V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 11th-order segments

# Polyhedron as Polyhedra Generator (segments trisection)

- Author:
- leucotea, Roman Chijner

- Topic:
- Solids or 3D Shapes

Let the vertices of the initial polyhedron belong to the same sphere. On its basis, can be constructed a certain series of polyhedra. The vertices of each of them are the points of the trisections of the segments of the original polyhedron that have the same length (calculated with a certain accuracy). Obviously, the number of vertices of the constructed polyhedron is twice the number of trisected segments and they all lie on the same sphere.

## Table of Contents

### ⓿. Biscribed Pentakis Dodecahedron

- Biscribed Pentakis Dodecahedron: The Icosahedron-Dodecahedron Compound whose all vertices lie on the same sphere
- Series of polyhedra obtained by trisection (truncation) segments of the original polyhedron
- Serie of polyhedra obtained by trisection (truncation) segments of the Biscribed Pentakis Dodecahedron
- Images. Series of polyhedra obtained by trisection (truncation) different segments of the original polyhedron

### ❶. Rhombicosidodecahedron (V=120) and its dual polyhedron- (V=122) from Biscribed Pentakis Dodecahedron for the case of trisection of its 1st-order segments

- Rhombicosidodecahedron from Biscribed Pentakis Dodecahedron for the case of trisection of its 1st-order segments
- Images . Rhombicosidodecahedron from Biscribed Pentakis Dodecahedron for the case of trisection of its 1st-order segments
- Images 1. Rhombicosidodecahedron from Biscribed Pentakis Dodecahedron for the case of trisection of its 1st-order segments
- Images 2. Rhombicosidodecahedron from Biscribed Pentakis Dodecahedron for the case of trisection of its 1st-order segments

### ❷. Truncated dodecahedron (V=60) and its dual polyhedron- Triakis icosahedron (V=32) from Biscribed Pentakis Dodecahedron for the case of trisection of its 2nd-order segments

- Truncated Dodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 2nd-order segments
- Images . Truncated dodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 2nd-order segments
- Images 1. Truncated dodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 2nd-order segments
- Images 2. Truncated dodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 2nd-order segments

### ❸. Truncated icosahedron (V=60) and its dual polyhedron- Pentakis dodecahedron (V=32) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments

- Truncated Icosahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments
- Images . Truncated icosahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments
- Images 1. Truncated icosahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments
- Images 2. Truncated icosahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments

### ❹. Truncated icosidodecahedron (V=120) and its dual polyhedron- Disdyakis triacontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 4th-order segments

- Truncated icosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 4th-order segments
- Images . Truncated icosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 4th-order segments
- Images 1. Truncated icosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 4th-order segments
- Images 2. Truncated icosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 4th-order segments

### ❺. Polyhedron(V=120) and its dual polyhedron (V=152) from Biscribed Pentakis Dodecahedron for the case of trisection of its 5th-order segments

- Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 5th-order segments
- Images . Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 5th-order segments
- Images 1. Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 5th-order segments
- Images 2. Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 5th-order segments

### ❻. Polyhedron(V=120) and its dual polyhedron (V=152) from Biscribed Pentakis Dodecahedron for the case of trisection of its 6th-order segments

- Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 6th-order segments
- Images . Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 6th-order segments
- Images 1. Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 6th-order segments
- Images 2. Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 6th-order segments

### ❼. The Great Rhombicosidodecahedron (V=120) and its dual Disdyakis triacontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 7th-order segments

- The Great Rhombicosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 7th-order segments
- Images . The Great Rhombicosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 7th-order segments
- Images 1. The Great Rhombicosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 7th-order segments
- Images 2. The Great Rhombicosidodecahedron (V=120) from Biscribed Pentakis Dodecahedron for the case of trisection of its 7th-order segments

### ❽. Rhombicosidodecahedron (V=60) and its dual Deltoidal Hexecontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 8th-order segments (Variant1)

- Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 8th-order segments(Variant1)
- Images . Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 8th-order segments(Variant1)
- Images 1. Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 8th-order segments(Variant1)
- Images 2. Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 8th-order segments(Variant1)

### ❾. Rhombicosidodecahedron (V=60) and its dual Deltoidal Hexecontahedron (V=62) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th-order segments(Variant2)

- Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th-order segments(Variant2)
- Images . Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th-order segments(Variant2)
- Images 1. Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th-order segments(Variant2)

### ❿. Polyhedron(V=120) and its dual Polyhedron(V=152) from Biscribed Pentakis Dodecahedron for the case of trisection of its 10th-order segments

- Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of a trisection of its 10th-order segments
- Images . Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of a trisection of its 10th-order segments
- Images 1. Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of a trisection of its 10th-order segments
- Images 2. Polyhedron(V=120) from Biscribed Pentakis Dodecahedron for the case of a trisection of its 10th-order segments

### ⓫. Biscribed Pentakis Dodecahedron (V=32) and its dual Biscribed Truncated Icosahedron(V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 11th-order segments