Rotate the view with the left mouse button, zoom with the scroll wheel or alt + left mouse button, and pan by clicking and dragging the right mouse button. Vertices can be dragged with left click. Change the radius up to which the chambers are displayed with the slider. Hovering over a chamber displays the canonical representative element for the stabiliser of the chamber.

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A spherical building of type A₂.

Represented group:	$\text{GL}_3(F_2)$ or $\text{SL}_3(F_2)$, with $F_2$ the field of order 2.
Stabiliser of the fundamental chamber:	$$B = \left\{ \begin{pmatrix}\nonumber *&*&*\\ 0&*&*\\ 0&0&* \end{pmatrix} \right\}$$
Simple reflections:	$s_0 = \begin{pmatrix}\nonumber 0&1&0\\ 1&0&0\\ 0&0&1 \end{pmatrix}$ $s_1 = \begin{pmatrix}\nonumber 1&0&0\\ 0&0&1\\ 0&1&0 \end{pmatrix}$

A spherical building of type A₃.

Represented group:	$\text{GL}_4(F_2)$ or $\text{SL}_4(F_2)$, with $F_2$ the field of order 2.
Stabiliser of the fundamental chamber:	$$B = \left\{ \begin{pmatrix}\nonumber *&*&*&*\\ 0&*&*&*\\ 0&0&*&*\\ 0&0&0&* \end{pmatrix} \right\}$$
Simple reflections:	$s_0 =\begin{pmatrix}\nonumber 0&1&0&0\\ 1&0&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{pmatrix}$ $s_1 =\begin{pmatrix}\nonumber 1&0&0&0\\ 0&0&1&0\\ 0&1&0&0\\ 0&0&0&1 \end{pmatrix}$ $s_2 =\begin{pmatrix}\nonumber 1&0&0&0\\ 0&1&0&0\\ 0&0&0&1\\ 0&0&1&0 \end{pmatrix}$

An affine building of type Ã₂.

Represented group:	$\text{GL}_3(\mathbb{Q}_2)$ or $\text{SL}_3(\mathbb{Q}_2)$, with $\mathbb{Q}_2$ the field of 2-adic numbers.
Stabiliser of the fundamental chamber:	$$B = \left\{ \begin{pmatrix}\nonumber \nu=0 &\nu\geq0 &\nu\geq0\\ \nu\geq1&\nu=0 &\nu\geq0\\ \nu\geq1&\nu\geq1 &\nu=0 \end{pmatrix} \right\}$$ where $\nu$ is the 2-adic valuation.
Simple reflections:	$s_0 =\begin{pmatrix}\nonumber 0&1&0\\ 1&0&0\\ 0&0&1 \end{pmatrix}$ $s_1 =\begin{pmatrix}\nonumber 1&0&0\\ 0&0&1\\ 0&1&0 \end{pmatrix}$ $s_2 =\begin{pmatrix}\nonumber 0 &0 &-\varpi^{-1}\\ 0 &1 &0\\ \varpi &0 &0 \end{pmatrix}$ Here, $\varpi$ is a choice of uniformizer of $\mathbb{Q}_2$.